In the paper, the authors establish several integral inequalities of the Ostrowski type for s-logarithmically convex functions. These integral inequalities modify the conditions and correct errors in two main theorems of the paper [A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math. J. 22 (2015), no. 1, 1–7].
在这篇论文中，作者为 s 对数凸函数建立了几个奥斯特洛夫斯基类型的积分不等式。这些积分不等式修改了论文 [A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logithmically convex functions] 中两个主要定理的条件并纠正了其中的错误。O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math.22 (2015), no. 1, 1-7].
{"title":"Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions","authors":"B. Xi, Shuhong Wang, Feng Qi","doi":"10.1515/gmj-2024-2018","DOIUrl":"https://doi.org/10.1515/gmj-2024-2018","url":null,"abstract":"\u0000 In the paper, the authors establish several integral inequalities of the Ostrowski type for s-logarithmically convex functions. These integral inequalities modify the conditions and correct errors in two main theorems of the paper [A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math. J.\u0000 22 (2015), no. 1, 1–7].","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140662718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we introduce Fibo-Pascal sequence spaces PpF{P_{p}^{F}}, 0<p<∞{0, and P∞F{P_{infty}^{F}} through the utilization of the Fibo-Pascal matrix PF{P^{F}}
在本文中，我们通过利用菲波帕斯卡矩阵 P F {P_{p}^{F}} 引入菲波帕斯卡序列空间 P p F {P_{p}^{F}} , 0 p ∞ {0 , 和 P ∞ F {P_{infty}^{F}} 通过利用 Fibo-Pascal 矩阵 P F {P^{F}}. .我们确定 P p F {P_{p}^{F}} 和 P ∞ F {P_{infty}^{F}} 都是 BK 空间，分别与经典空间 ℓ p {ell_{p} 和 ℓ ∞ {ell_{infty}} 具有线性同构性。｝ 分别。为了进一步加深研究，我们将继续推导 P p F {P_{p}^{F} 空间的 Schauder 基础，并对其进行详尽的计算。｝ 同时，我们还详尽计算了 P p F {P_{p}^{F} 和 P ∞ F {P_{infty}^{F} 两个空间的 α-、β- 和 γ 对偶。｝ .此外，我们还负责描述与空间 P p F {P_{p}^{F}} 和 P ∞ F {P_{infty}^{F}} 有关的某些矩阵映射类别。 .本研究的最后一节将专门讨论
{"title":"A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness","authors":"M. C. Dağlı, Taja Yaying","doi":"10.1515/gmj-2024-2021","DOIUrl":"https://doi.org/10.1515/gmj-2024-2021","url":null,"abstract":"\u0000 <jats:p>In this article, we introduce Fibo-Pascal sequence spaces <jats:inline-formula id=\"j_gmj-2024-2021_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msubsup>\u0000 <m:mi>P</m:mi>\u0000 <m:mi>p</m:mi>\u0000 <m:mi>F</m:mi>\u0000 </m:msubsup>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2021_eq_0255.png\" />\u0000 <jats:tex-math>{P_{p}^{F}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>, <jats:inline-formula id=\"j_gmj-2024-2021_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mn>0</m:mn>\u0000 <m:mo><</m:mo>\u0000 <m:mi>p</m:mi>\u0000 <m:mo><</m:mo>\u0000 <m:mi mathvariant=\"normal\">∞</m:mi>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2021_eq_0223.png\" />\u0000 <jats:tex-math>{0<p<infty}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>, and <jats:inline-formula id=\"j_gmj-2024-2021_ineq_9997\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msubsup>\u0000 <m:mi>P</m:mi>\u0000 <m:mi mathvariant=\"normal\">∞</m:mi>\u0000 <m:mi>F</m:mi>\u0000 </m:msubsup>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2021_eq_0253.png\" />\u0000 <jats:tex-math>{P_{infty}^{F}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> through the utilization of the Fibo-Pascal matrix <jats:inline-formula id=\"j_gmj-2024-2021_ineq_9996\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msup>\u0000 <m:mi>P</m:mi>\u0000 <m:mi>F</m:mi>\u0000 </m:msup>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2021_eq_0250.png\" />\u0000 <jats:tex-math>{P^{F}}</jats:tex-math>\u0000 </jats:al","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140663344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu, Wu and Leng defined the quasi Lp{L_{p}}-intersection bodies. In this paper, we consider the polar dualities and star dualities of quasi Lp{L_{p}}-intersection bodies and establish some related inequalities.
Yu、Wu 和 Leng 定义了准 L p {L_{p}} 交点体。 -本文考虑了准 L p {L_{p}} 交点体的极对偶性和星对偶性，并建立了一些相关的不等式。 -本文考虑了准 L p {L_{p}} 交点体的极对偶性和星对偶性，并建立了一些相关的不等式。
{"title":"On the polar dualities and star dualities of the quasi Lp\u0000 -intersection bodies","authors":"Yanping Zhou, Weidong Wang","doi":"10.1515/gmj-2024-2019","DOIUrl":"https://doi.org/10.1515/gmj-2024-2019","url":null,"abstract":"\u0000 <jats:p>Yu, Wu and Leng defined the quasi <jats:inline-formula id=\"j_gmj-2024-2019_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msub>\u0000 <m:mi>L</m:mi>\u0000 <m:mi>p</m:mi>\u0000 </m:msub>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2019_eq_0094.png\" />\u0000 <jats:tex-math>{L_{p}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-intersection bodies.\u0000In this paper, we consider the polar dualities and star dualities of quasi <jats:inline-formula id=\"j_gmj-2024-2019_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msub>\u0000 <m:mi>L</m:mi>\u0000 <m:mi>p</m:mi>\u0000 </m:msub>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2019_eq_0094.png\" />\u0000 <jats:tex-math>{L_{p}}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-intersection bodies and establish some related inequalities.</jats:p>","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140659733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove a lower bound estimate for capacities in Hajłasz–Besov, Hajłasz–Triebel–Lizorkin and Hajłasz–Sobolev spaces with generalized smoothness defined on metric spaces in terms of Netrusov–Hausdorff content or Hausdorff content. These results are improvements of the results obtained in [Z. Li, D. Yang and W. Yuan, Lebesgue points of Besov and Triebel–Lizorkin spaces with generalized smoothness, Mathematics 9 2021, 10.3390/math9212724].
我们证明了哈伊瓦斯-贝索夫空间、哈伊瓦斯-特里贝尔-利佐尔金空间和哈伊瓦斯-索博列夫空间中容量的下界估计，这些空间具有以内特鲁索夫-豪斯多夫含量或豪斯多夫含量定义在度量空间上的广义光滑度。这些结果是对［Z. Li, D. Yang and W.Li, D. Yang and W. Yuan, Lebesgue points of Besov and Triebel-Lizorkin spaces with generalized smoothness, Mathematics 9 2021, 10.3390/math9212724].
{"title":"Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness","authors":"Nijjwal Karak, Debarati Mondal","doi":"10.1515/gmj-2024-2015","DOIUrl":"https://doi.org/10.1515/gmj-2024-2015","url":null,"abstract":"\u0000 We prove a lower bound estimate for capacities in Hajłasz–Besov, Hajłasz–Triebel–Lizorkin and Hajłasz–Sobolev spaces with generalized smoothness defined on metric spaces in terms of Netrusov–Hausdorff content or Hausdorff content. These results are improvements of the results obtained in [Z. Li, D. Yang and W. Yuan, Lebesgue points of Besov and Triebel–Lizorkin spaces with generalized smoothness,\u0000Mathematics 9 2021, 10.3390/math9212724].","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140661466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we improve some Berezin number inequalities concerning a Hilbert space. It is shown that if T is a bounded linear operator on a Hilbert space, then for any r≥1{rgeq 1}, 𝐛𝐞𝐫2r(T)≤12𝐛𝐞𝐫r(|T*|2(1-t)|T|2t)+14∥|T|4rt+|T*|4r(1-t)∥𝐛𝐞𝐫(0≤t≤1),mathbf{ber}^{2r}(T)leqfrac{1}{2}mathbf{ber}^{r}({{|{{T}^{*}}|}^{2(1-t)}}{{% |T|}^{2t}})+frac{1}{4}{{|{{|T|}^{4rt}}+{{|{{T}^{*}}|}^{4r(1-t)}}|}_{mathbf% {ber}}}quad(0leq tleq 1), where
在本文中，我们改进了一些关于希尔伯特空间的贝雷津数不等式。结果表明，如果 T 是希尔伯特空间上的有界线性算子，那么对于任意 r ≥ 1 {rgeq 1} ，𝐛𝐞𝐫𝐫是有界线性算子。 𝐛𝐞𝐫 2 r ( T ) ≤ 1 2 𝐛𝐞𝐫 r ( | T * | 2 ( 1 - t ) | T | 2 t ) + 1 4 ∥ | T | 4 r t + | T * | 4 r ( 1 - t ) ∥ 𝐛𝐞𝐫 ( 0 ≤ t ≤ 1 ) 、 mathbf{ber}^{2r}(T)leqfrac{1}{2}mathbf{ber}^{r}({{|{{T}^{*}}|}^{2(1-t)}}{{% |T|}^{2t}})+frac{1}{4}{{|{{|T|}^{4rt}}+{{|{{T}^{*}}|}^{4r(1-t)}}|}_{mathbf% {ber}}}quad(0leq tleq 1), 其中 | T | = ( T * T ) 1 2 {|T|={{({{T}^{*}}T)}^{frac{1}{2}}}} .
{"title":"New estimates for the Berezin number of Hilbert space operators","authors":"Parvaneh Zolfaghari","doi":"10.1515/gmj-2024-2012","DOIUrl":"https://doi.org/10.1515/gmj-2024-2012","url":null,"abstract":"In this article, we improve some Berezin number inequalities concerning a Hilbert space. It is shown that if <jats:italic>T</jats:italic> is a bounded linear operator on a Hilbert space, then for any <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>r</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2012_eq_0198.png\" /> <jats:tex-math>{rgeq 1}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:disp-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>𝐛𝐞𝐫</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>r</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>T</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>≤</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:msup> <m:mi>𝐛𝐞𝐫</m:mi> <m:mi>r</m:mi> </m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mo stretchy=\"false\">|</m:mo> <m:msup> <m:mi>T</m:mi> <m:mo>*</m:mo> </m:msup> <m:msup> <m:mo stretchy=\"false\">|</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>-</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:msup> <m:mo stretchy=\"false\">|</m:mo> <m:mi>T</m:mi> <m:msup> <m:mo stretchy=\"false\">|</m:mo> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>t</m:mi> </m:mrow> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>4</m:mn> </m:mfrac> <m:mo>∥</m:mo> <m:mo stretchy=\"false\">|</m:mo> <m:mi>T</m:mi> <m:msup> <m:mo stretchy=\"false\">|</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mo></m:mo> <m:mi>r</m:mi> <m:mo></m:mo> <m:mi>t</m:mi> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:mo stretchy=\"false\">|</m:mo> <m:msup> <m:mi>T</m:mi> <m:mo>*</m:mo> </m:msup> <m:msup> <m:mo stretchy=\"false\">|</m:mo> <m:mrow> <m:mn>4</m:mn> <m:mo></m:mo> <m:mi>r</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>-</m:mo> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:msup> <m:msub> <m:mo>∥</m:mo> <m:mi>𝐛𝐞𝐫</m:mi> </m:msub> <m:mo mathvariant=\"italic\" separator=\"true\"> </m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mn>0</m:mn> <m:mo>≤</m:mo> <m:mi>t</m:mi> <m:mo>≤</m:mo> <m:mn>1</m:mn> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:math> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2012_eq_0060.png\" /> <jats:tex-math>mathbf{ber}^{2r}(T)leqfrac{1}{2}mathbf{ber}^{r}({{|{{T}^{*}}|}^{2(1-t)}}{{% |T|}^{2t}})+frac{1}{4}{{|{{|T|}^{4rt}}+{{|{{T}^{*}}|}^{4r(1-t)}}|}_{mathbf% {ber}}}quad(0leq tleq 1),</jats:tex-math> </jats:alternatives> </jats:disp-formula> where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo ","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammed Zerra, Karim Bouchannafa, Lahcen Oukhtite
The main purpose of this paper is to scrutinize the deportment of generalized derivations of R satisfying some functional *{*}-identities involving the center of the factor ring R/P{R/P} where P is a prime ideal of the ring R. Moreover, we suggest to give generalization of some well known results.
本文的主要目的是仔细研究满足某些函数 * {*} -identities 的 R 的广义派生的描述。 -此外，我们建议对一些众所周知的结果进行概括。
{"title":"On generalized derivations in factor rings","authors":"Mohammed Zerra, Karim Bouchannafa, Lahcen Oukhtite","doi":"10.1515/gmj-2024-2017","DOIUrl":"https://doi.org/10.1515/gmj-2024-2017","url":null,"abstract":"The main purpose of this paper is to scrutinize the deportment of generalized derivations of <jats:italic>R</jats:italic> satisfying some functional <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>*</m:mo> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2017_eq_0051.png\" /> <jats:tex-math>{*}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-identities involving the center of the factor ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>R</m:mi> <m:mo>/</m:mo> <m:mi>P</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2017_eq_0081.png\" /> <jats:tex-math>{R/P}</jats:tex-math> </jats:alternatives> </jats:inline-formula> where <jats:italic>P</jats:italic> is a prime ideal of the ring <jats:italic>R</jats:italic>. Moreover, we suggest to give generalization of some well known results.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain 2×2{2times 2} block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (Comm. Algebra 48 (2020), 676–690) and Benítez, Liu and Zhu (Linear Multilinear Algebra 59 (2011), 279–289).
{"title":"Group invertibility of the sum in rings and its applications","authors":"Huanyin Chen, Dayong Liu, Marjan Sheibani","doi":"10.1515/gmj-2024-2010","DOIUrl":"https://doi.org/10.1515/gmj-2024-2010","url":null,"abstract":"We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>2</m:mn> <m:mo>×</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2010_eq_0193.png\" /> <jats:tex-math>{2times 2}</jats:tex-math> </jats:alternatives> </jats:inline-formula> block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (<jats:italic>Comm. Algebra</jats:italic> 48 (2020), 676–690) and Benítez, Liu and Zhu (<jats:italic>Linear Multilinear Algebra</jats:italic> 59 (2011), 279–289).","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The spherical mean operator has been widely studied and has seen remarkable development in many areas of harmonic analysis. In this paper, we consider the Stockwell transform related to the spherical mean operator. Since the study of time-frequency analysis is both theoretically interesting and practically useful, we will study several problems for the generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transformation. Next, we will study the boundedness and then the compactness of localization operators related to the generalized Stockwell transform, and finally we will introduce and study its scalogram.
{"title":"Generalized Stockwell transforms: Spherical mean operators and applications","authors":"Saifallah Ghobber, Hatem Mejjaoli","doi":"10.1515/gmj-2024-2014","DOIUrl":"https://doi.org/10.1515/gmj-2024-2014","url":null,"abstract":"The spherical mean operator has been widely studied and has seen remarkable development in many areas of harmonic analysis. In this paper, we consider the Stockwell transform related to the spherical mean operator. Since the study of time-frequency analysis is both theoretically interesting and practically useful, we will study several problems for the generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transformation. Next, we will study the boundedness and then the compactness of localization operators related to the generalized Stockwell transform, and finally we will introduce and study its scalogram.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weak type estimates for genuine Calderón–Zygmund operators are established on the local Morrey spaces associated with ball quasi-Banach function spaces by two different methods. Above all, we obtain weak type estimates for the operator on the local weak Morrey spaces with variable exponents.
{"title":"Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces","authors":"Mingwei Shi, Jiang Zhou, Songbai Wang","doi":"10.1515/gmj-2024-2013","DOIUrl":"https://doi.org/10.1515/gmj-2024-2013","url":null,"abstract":"Weak type estimates for genuine Calderón–Zygmund operators are established on the local Morrey spaces associated with ball quasi-Banach function spaces by two different methods. Above all, we obtain weak type estimates for the operator on the local weak Morrey spaces with variable exponents.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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