{"title":"Some remarks on the Boyd functions related to the admissible sequences","authors":"Thomas Lamby, S. Nicolay","doi":"10.4171/zaa/1705","DOIUrl":"https://doi.org/10.4171/zaa/1705","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46364409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
José R. Fernández, Santwana Mukhopadhyay, R. Quintanilla, Om Namha Shivay
{"title":"On the existence and decay in a new thermoelastic theory with two temperatures","authors":"José R. Fernández, Santwana Mukhopadhyay, R. Quintanilla, Om Namha Shivay","doi":"10.4171/zaa/1702","DOIUrl":"https://doi.org/10.4171/zaa/1702","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48792775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiplicity of solutions for a singular system involving the fractional $p-q$-Laplacian operator and sign-changing weight functions","authors":"N. T. Chung, A. Ghanmi","doi":"10.4171/zaa/1701","DOIUrl":"https://doi.org/10.4171/zaa/1701","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":"11 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41266010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note we consider weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work [4]. We provide a complete characterization of when these spaces are ultrabornological and barrelled in terms of the defining weight system, thereby improving the main Theorem 5.1 of [4]. In particular, we obtain that the multiplier space of the Gelfand-Shilov space $Sigma^{r}_{s}(mathbb{R}^{d})$ of Beurling type is ultrabornological, whereas the one of the Gelfand-Shilov space $mathcal{S}^{r}_{s}(mathbb{R}^{d})$ of Roumieu type is not barrelled.
{"title":"A note on the barrelledness of weighted PLB-spaces of ultradifferentiable functions","authors":"A. Debrouwere, L. Neyt","doi":"10.4171/zaa/1711","DOIUrl":"https://doi.org/10.4171/zaa/1711","url":null,"abstract":"In this note we consider weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work [4]. We provide a complete characterization of when these spaces are ultrabornological and barrelled in terms of the defining weight system, thereby improving the main Theorem 5.1 of [4]. In particular, we obtain that the multiplier space of the Gelfand-Shilov space $Sigma^{r}_{s}(mathbb{R}^{d})$ of Beurling type is ultrabornological, whereas the one of the Gelfand-Shilov space $mathcal{S}^{r}_{s}(mathbb{R}^{d})$ of Roumieu type is not barrelled.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44169922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the Cauchy problem for the inhomogeneous biharmonic nonlinear Schr¨odinger (IBNLS) equation where d ∈ N , s ≥ 0, 0 < b < 4, σ > 0 and λ ∈ R . Under some regularity assumption for the nonlinear term, we prove that the IBNLS equation is locally well-posed in H s ( R d ) if d ∈ N , 0 ≤ s < min { 2 + d 2 , 32 d } , 0 < b < min { 4 , d, 32 d − s, d 2 + 2 − s } and 0 < σ < σ c ( s ). Here σ c ( s ) = 8 − 2 b d − 2 s if s < d 2 , and σ c ( s ) = ∞ if s ≥ d 2 . Our local well-posedness result improves the ones of Guzm´an-Pastor [Nonlinear Anal. Real World Appl. 56 (2020) 103174] and Liu-Zhang [J. Differential Equations 296 (2021) 335-368] by extending the validity of s and b . Mathematics Subject Classification (2020) . Primary 35Q55; Secondary 35A01.
本文研究了d∈N, s≥0,0 < b < 4， σ > 0， λ∈R的非齐次双调和非线性Schr¨odinger (IBNLS)方程的Cauchy问题。在非线性项的一些正则性假设下，证明了当d∈N, 0≤s < min {2 + d 2,32 d}， 0 < b < min {4, d, 32 d - s, d 2 + 2 - s}和0 < σ < σ c (s)时IBNLS方程在H s (R d)中是局部适定的。如果s < d2，则σ c (s) = 8−2 b d−2 s，如果s≥d2，则σ c (s) =∞。我们的局部适定性结果改进了Guzm´an-Pastor[非线性分析]的结果。[J] .中国科学:自然科学，2016,35(1):1 - 4。微分方程296(2021)335-368]通过扩展s和b的有效性。数学学科分类(2020)。主要35 q55;二次35 a01。
{"title":"Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces","authors":"J. An, PyongJo Ryu, Jinmyong Kim","doi":"10.4171/zaa/1707","DOIUrl":"https://doi.org/10.4171/zaa/1707","url":null,"abstract":"In this paper, we study the Cauchy problem for the inhomogeneous biharmonic nonlinear Schr¨odinger (IBNLS) equation where d ∈ N , s ≥ 0, 0 < b < 4, σ > 0 and λ ∈ R . Under some regularity assumption for the nonlinear term, we prove that the IBNLS equation is locally well-posed in H s ( R d ) if d ∈ N , 0 ≤ s < min { 2 + d 2 , 32 d } , 0 < b < min { 4 , d, 32 d − s, d 2 + 2 − s } and 0 < σ < σ c ( s ). Here σ c ( s ) = 8 − 2 b d − 2 s if s < d 2 , and σ c ( s ) = ∞ if s ≥ d 2 . Our local well-posedness result improves the ones of Guzm´an-Pastor [Nonlinear Anal. Real World Appl. 56 (2020) 103174] and Liu-Zhang [J. Differential Equations 296 (2021) 335-368] by extending the validity of s and b . Mathematics Subject Classification (2020) . Primary 35Q55; Secondary 35A01.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46189997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a Banach space $X$ and an additional coarser Hausdorff locally convex topology $tau$ on $X$ we characterise the generators of $tau$-bi-continuous semigroups in the spirit of the Lumer--Phillips theorem, i.e. by means of dissipativity w.r.t.~a directed system of seminorms and a range condition.
{"title":"A note on the Lumer–Phillips theorem for bi-continuous semigroups","authors":"K. Kruse, C. Seifert","doi":"10.4171/ZAA/1709","DOIUrl":"https://doi.org/10.4171/ZAA/1709","url":null,"abstract":"Given a Banach space $X$ and an additional coarser Hausdorff locally convex topology $tau$ on $X$ we characterise the generators of $tau$-bi-continuous semigroups in the spirit of the Lumer--Phillips theorem, i.e. by means of dissipativity w.r.t.~a directed system of seminorms and a range condition.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45584512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integration with respect to Baire vector measures with applications to the spectral theory","authors":"M. Nowak","doi":"10.4171/zaa/1696","DOIUrl":"https://doi.org/10.4171/zaa/1696","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48687614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Uniform regularity for a density-dependent incompressible Gross–Pitaevskii–Navier–Stokes system","authors":"Jishan Fan, G. Nakamura, T. Tang","doi":"10.4171/zaa/1694","DOIUrl":"https://doi.org/10.4171/zaa/1694","url":null,"abstract":"","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44851231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We prove that a function in several variables is in the local Zyg- mund class Z m, 1 if and only if its composite with every smooth curve is of class Z m, 1 . This complements the well-known analogous result for local H¨older– Lipschitz classes C m,α which we reprove along the way. We demonstrate that these results generalize to mappings between Banach spaces and use them to study the regularity of the superposition operator f ∗ : g 7→ f ◦ g acting on the Zygmund space Λ m +1 ( R d ). We prove that, for all integers m,k k, R ).
{"title":"Hölder–Zygmund classes on smooth curves","authors":"A. Rainer","doi":"10.4171/zaa/1704","DOIUrl":"https://doi.org/10.4171/zaa/1704","url":null,"abstract":". We prove that a function in several variables is in the local Zyg- mund class Z m, 1 if and only if its composite with every smooth curve is of class Z m, 1 . This complements the well-known analogous result for local H¨older– Lipschitz classes C m,α which we reprove along the way. We demonstrate that these results generalize to mappings between Banach spaces and use them to study the regularity of the superposition operator f ∗ : g 7→ f ◦ g acting on the Zygmund space Λ m +1 ( R d ). We prove that, for all integers m,k k, R ).","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49060885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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