Pub Date : 2023-01-01DOI: 10.59849/2218-6816.2023.2.200
D. Bród, A. Szynal-Liana
{"title":"On Bihypernomials Related to Balancing and Chebyshev Polynomials","authors":"D. Bród, A. Szynal-Liana","doi":"10.59849/2218-6816.2023.2.200","DOIUrl":"https://doi.org/10.59849/2218-6816.2023.2.200","url":null,"abstract":"","PeriodicalId":54116,"journal":{"name":"Azerbaijan Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71244524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.59849/2218-6816.2023.2.100
A. Khanmamedov, D. H. Orudjov
{"title":"Triangular Representation of the Solution to the Schrodinger Equation with an Additional Linear Potential","authors":"A. Khanmamedov, D. H. Orudjov","doi":"10.59849/2218-6816.2023.2.100","DOIUrl":"https://doi.org/10.59849/2218-6816.2023.2.100","url":null,"abstract":"","PeriodicalId":54116,"journal":{"name":"Azerbaijan Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71244309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.59849/2218-6816.2023.2.120
N. Elharrar, J. Igbida
{"title":"Rothe Time-Discretization Method for Nolinear Parabolic Problems in Weighted Sobolev Space with Variable Exponents","authors":"N. Elharrar, J. Igbida","doi":"10.59849/2218-6816.2023.2.120","DOIUrl":"https://doi.org/10.59849/2218-6816.2023.2.120","url":null,"abstract":"","PeriodicalId":54116,"journal":{"name":"Azerbaijan Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71244376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-26DOI: 10.59849/2218-6816.2023.2.51
R. Mustafayev, Nevin Bilgiccli, M. Yılmaz
In this paper we calculate the norm of the generalized maximal operator $M_{phi,Lambda^{alpha}(b)}$, defined with $0
本文计算了广义极大算子$M_{phi，Lambda^{alpha}(b)}$的范数，定义为$0
{"title":"Norms of Maximal Functions between Generalized and Classical Lorentz Spaces","authors":"R. Mustafayev, Nevin Bilgiccli, M. Yılmaz","doi":"10.59849/2218-6816.2023.2.51","DOIUrl":"https://doi.org/10.59849/2218-6816.2023.2.51","url":null,"abstract":"In this paper we calculate the norm of the generalized maximal operator $M_{phi,Lambda^{alpha}(b)}$, defined with $0<alpha<infty$ and functions $b,,phi: (0,infty) rightarrow (0,infty)$ for all measurable functions $f$ on ${mathbb R}^n$ by begin{equation*} M_{phi,Lambda^{alpha}(b)}f(x) : = sup_{Q ni x} frac{|f chi_Q|_{Lambda^{alpha}(b)}}{phi (|Q|)}, qquad x in {mathbb R}^n, end{equation*} from ${operatorname{GGamma}}(p,m,v)$ into $Lambda^q(w)$. Here $Lambda^{alpha}(b)$ and ${operatorname{GGamma}}(p,m,w)$ are the classical and generalized Lorentz spaces, defined as a set of all measurable functions $f$ defined on ${mathbb R}^n$ for which $$ |f|_{Lambda^{alpha}(b)} = bigg( int_0^{infty} [f^*(s)]^{alpha} b(s),ds bigg)^{frac{1}{alpha}}<infty quad mbox{and} quad |f|_{{operatorname{GGamma}}(p,m,w)} = bigg( int_0^{infty} bigg( int_0^x [f^* (tau)]^p,dtau bigg)^{frac{m}{p}} v(x),dx bigg)^{frac{1}{m}}<infty, $$ respectively. We reduce the problem to the solution of the inequality begin{equation*} bigg( int_0^{infty} big[ T_{u,b}f^* (x)big]^q , w(x),dxbigg)^{frac{1}{q}} le C , bigg( int_0^{infty} bigg( int_0^x [f^* (tau)]^p,dtau bigg)^{frac{m}{p}} v(x),dx bigg)^{frac{1}{m}} end{equation*} where $w$ and $v$ are weight functions on $(0,infty)$. Here $f^*$ is the non-increasing rearrangement of $f$ defined on ${mathbb R}^n$ and $T_{u,b}$ is the iterated Hardy-type operator involving suprema, which is defined for a measurable non-negative function $f$ on $(0,infty)$ by $$ (T_{u,b} g)(t) : = sup_{tau in [t,infty)} frac{u(tau)}{B(tau)} int_0^{tau} g(s)b(s),ds,qquad t in (0,infty), $$ where $u$ and $b$ are appropriate weight functions on $(0,infty)$ and the function $B(t) : = int_0^t b(s),ds$ satisfies $0","PeriodicalId":54116,"journal":{"name":"Azerbaijan Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45007311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-06-06DOI: 10.1017/cbo9781316408124
A. Pinkus
In this paper we survey some of the basic properties of linear combinationsof ridge functions.
本文研究了脊函数线性组合的一些基本性质。
{"title":"On Ridge Functions","authors":"A. Pinkus","doi":"10.1017/cbo9781316408124","DOIUrl":"https://doi.org/10.1017/cbo9781316408124","url":null,"abstract":"In this paper we survey some of the basic properties of linear combinationsof ridge functions.","PeriodicalId":54116,"journal":{"name":"Azerbaijan Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2013-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57121910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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