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Octahedrality and Gâteaux smoothness 八面体性和伽陀平滑性
arXiv - MATH - Functional Analysis Pub Date : 2024-08-07 DOI: arxiv-2408.03737
Ch. Cobollo, P. Hájek
{"title":"Octahedrality and Gâteaux smoothness","authors":"Ch. Cobollo, P. Hájek","doi":"arxiv-2408.03737","DOIUrl":"https://doi.org/arxiv-2408.03737","url":null,"abstract":"We prove that every Banach space admitting a Gateaux smooth norm and\u0000containing a complemented copy of $ell_1$ has an equivalent renorming which is\u0000simultaneously G^ateaux smooth and octahedral. This is a partial solution to a\u0000problem from the early nineties.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"194 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930633","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}
引用次数: 0
On collectively $σ$-Levi sets of operators 论算子的集合σ$-列维集
arXiv - MATH - Functional Analysis Pub Date : 2024-08-07 DOI: arxiv-2408.03686
Eduard Emelyanov
{"title":"On collectively $σ$-Levi sets of operators","authors":"Eduard Emelyanov","doi":"arxiv-2408.03686","DOIUrl":"https://doi.org/arxiv-2408.03686","url":null,"abstract":"A collectively $sigma$-Levi set of operators is a generalization of the\u0000$sigma$-Levi operator. By use of collective order convergence, we investigate\u0000relations between collectively $sigma$-Levi and collectively compact sets of\u0000operators.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"304 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930554","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}
引用次数: 0
Boundedness of New Type Fourier Integral Operators with Product Structure 具有积结构的新型傅里叶积分算子的有界性
arXiv - MATH - Functional Analysis Pub Date : 2024-08-06 DOI: arxiv-2408.03211
Chaoqiang Tan, Zipeng Wang
{"title":"Boundedness of New Type Fourier Integral Operators with Product Structure","authors":"Chaoqiang Tan, Zipeng Wang","doi":"arxiv-2408.03211","DOIUrl":"https://doi.org/arxiv-2408.03211","url":null,"abstract":"We investigate a class of Fourier integral operators with weakened symbols,\u0000which satisfy a multi-parameter differential inequality in $R^n$. We establish\u0000that these operators retain the classical $L^p$ boundedness and the $H^1$ to\u0000$L^1$ boundedness. Notably, the Hardy space considered here is the traditional\u0000single-parameter Hardy space rather than a product Hardy space.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930559","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}
引用次数: 0
Rhaly operators: more on generalized Cesàro operators 雷利算子：关于广义塞萨罗算子的更多信息
arXiv - MATH - Functional Analysis Pub Date : 2024-08-06 DOI: arxiv-2408.03182
Eva A. Gallardo-Gutiérrez, Jonathan R. Partington
{"title":"Rhaly operators: more on generalized Cesàro operators","authors":"Eva A. Gallardo-Gutiérrez, Jonathan R. Partington","doi":"arxiv-2408.03182","DOIUrl":"https://doi.org/arxiv-2408.03182","url":null,"abstract":"Rhaly operators, as generalizations of the Ces`aro operator, are studied\u0000from the standpoint of view of spectral theory and invariant subspaces,\u0000extending previous results by Rhaly and Leibowitz to a framework where\u0000generalized Ces`aro operators arise naturally.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930564","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}
引用次数: 0
Excess of Fusion Frames: A Comprehensive Approach 融合框架过剩：综合方法
arXiv - MATH - Functional Analysis Pub Date : 2024-08-06 DOI: arxiv-2408.03179
Ehsan Ameli, Ali Akbar Arefijamaal, Fahimeh Arabyani Neyshaburi
{"title":"Excess of Fusion Frames: A Comprehensive Approach","authors":"Ehsan Ameli, Ali Akbar Arefijamaal, Fahimeh Arabyani Neyshaburi","doi":"arxiv-2408.03179","DOIUrl":"https://doi.org/arxiv-2408.03179","url":null,"abstract":"Computing the excess as a method of measuring the redundancy of frames was\u0000recently introduced to address certain issues in frame theory. In this paper,\u0000the concept of excess for the fusion frame setting is studied. Initially, a\u0000local approach is presented to determine exactly which part of each subspace\u0000should be considered as redundancy. Then, several explicit methods are provided\u0000to compute the excess of fusion frames and their $Q$-duals. In particular, some\u0000upper bounds for the excess of $Q$-dual fusion frames are established. It turns\u0000out that each fusion frame and its $Q$-dual may not necessarily have the same\u0000excess. Along the way, unlike ordinary frames, it follows that for every $n in\u0000Bbb{N}$, we can provide a fusion frame together an its $Q$-dual such that the\u0000difference of their excess is $n$. Furthermore, the connection between the\u0000excess of fusion frames and their orthogonal complement fusion frames are\u0000completely characterized. Finally, several examples are exhibited to confirm\u0000the obtained results.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930562","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}
引用次数: 0
Extension of Localisation Operators to Ultradistributional Symbols With Super-Exponential Growth 将定位算子扩展至超指数增长的超分布符号
arXiv - MATH - Functional Analysis Pub Date : 2024-08-05 DOI: arxiv-2408.02437
Stevan Pilipović, Bojan Prangoski, Đorđe Vučković
{"title":"Extension of Localisation Operators to Ultradistributional Symbols With Super-Exponential Growth","authors":"Stevan Pilipović, Bojan Prangoski, Đorđe Vučković","doi":"arxiv-2408.02437","DOIUrl":"https://doi.org/arxiv-2408.02437","url":null,"abstract":"In the Gelfand-Shilov setting, the localisation operator\u0000$A^{varphi_1,varphi_2}_a$ is equal to the Weyl operator whose symbol is the\u0000convolution of $a$ with the Wigner transform of the windows $varphi_2$ and\u0000$varphi_1$. We employ this fact, to extend the definition of localisation\u0000operators to symbols $a$ having very fast super-exponential growth by allowing\u0000them to be mappings from ${mathcal D}^{{M_p}}(mathbb R^d)$ into ${mathcal\u0000D}'^{{M_p}}(mathbb R^d)$, where $M_p$, $pinmathbb N$, is a\u0000non-quasi-analytic Gevrey type sequence. By choosing the windows $varphi_1$\u0000and $varphi_2$ appropriately, our main results show that one can consider\u0000symbols with growth in position space of the form $exp(exp(l|cdot|^q))$,\u0000$l,q>0$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930557","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}
引用次数: 0
Distributions in spaces with thick submanifolds 具有厚子曲面的空间中的分布
arXiv - MATH - Functional Analysis Pub Date : 2024-08-05 DOI: arxiv-2408.02864
Jiajia Ding, Jasson Vindas, Yunyun Yang
{"title":"Distributions in spaces with thick submanifolds","authors":"Jiajia Ding, Jasson Vindas, Yunyun Yang","doi":"arxiv-2408.02864","DOIUrl":"https://doi.org/arxiv-2408.02864","url":null,"abstract":"This article generalizes the results of [J. Math. Anal. Appl. 512 (2022),\u0000Article No. 126075], which presented a theory of distributions (generalized\u0000functions) with a singular curve contained in the domain of the test functions.\u0000In this present article we construct a theory of distributions in\u0000$mathbb{R}^n$ with a ``thick submanifold'', that is, a new theory of thick\u0000distributions in $mathbb{R}^n$ whose domain contains a submanifold on which\u0000test functions may be singular.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930634","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}
引用次数: 0
The spherical maximal operators on hyperbolic spaces 双曲空间上的球面最大算子
arXiv - MATH - Functional Analysis Pub Date : 2024-08-05 DOI: arxiv-2408.02180
Peng Chen, Minxing Shen, Yunxiang Wang, Lixin Yan
{"title":"The spherical maximal operators on hyperbolic spaces","authors":"Peng Chen, Minxing Shen, Yunxiang Wang, Lixin Yan","doi":"arxiv-2408.02180","DOIUrl":"https://doi.org/arxiv-2408.02180","url":null,"abstract":"In this article we investigate $L^p$ boundedness of the spherical maximal\u0000operator $mathfrak{m}^alpha$ of (complex) order $alpha$ on the\u0000$n$-dimensional hyperbolic space $mathbb{H}^n$, which was introduced and\u0000studied by Kohen [13]. We prove that when $ngeq 2$, for $alphainmathbb{R}$\u0000and $1<p<infty$, if begin{eqnarray*}\u0000|mathfrak{m}^alpha(f)|_{L^p(mathbb{H}^n)}leq C|f|_{L^p(mathbb{H}^n)},\u0000end{eqnarray*} then we must have $alpha>1-n+n/p$ for $1<pleq 2$; or\u0000$alphageq max{1/p-(n-1)/2,(1-n)/p}$ for $2<p<infty$. Furthermore, we\u0000improve the result of Kohen [13, Theorem 3] by showing that\u0000$mathfrak{m}^alpha$ is bounded on $L^p(mathbb{H}^n)$ provided that\u0000$mathop{mathrm{Re}} alpha> max {{(2-n)/p}-{1/(p p_n)}, {(2-n)/p} -\u0000(p-2)/ [p p_n(p_n-2) ] } $ for $2leq pleq infty$, with $p_n=2(n+1)/(n-1)$\u0000for $ngeq 3$ and $p_n=4$ for $n=2$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930560","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}
引用次数: 0
The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators 广义大维纳汞齐空间和哈代-利特尔伍德最大算子的有界性
arXiv - MATH - Functional Analysis Pub Date : 2024-08-05 DOI: arxiv-2408.02406
A. Turan Gürkanlı
{"title":"The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators","authors":"A. Turan Gürkanlı","doi":"arxiv-2408.02406","DOIUrl":"https://doi.org/arxiv-2408.02406","url":null,"abstract":"Let $1<p,q<infty$ and let $a(x), b(x)$ be weight functions. In the present\u0000paper we define and investigate some basic properties of generalized grand\u0000Wiener amalgam space $W( L^{p),theta_1}(mathbb R^{n})),\u0000L^{q),theta_2}(mathbb R^{n})),$ where generalized grand Lebesgue spaces\u0000$L_{a}^{p)}(mathbb R^{n})$ and $L_{b}^{q)}(mathbb R^{n}),$ are local and\u0000global components, respectively. Next we study embeddings for these spaces,\u0000also we give some more properties of these spaces. At the end of this work, we\u0000discuss boundedness and unboundedness of the Hardy-Littlewood maximal operator\u0000between some generalized grand Wiener amalgam spaces.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969804","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}
引用次数: 0
Approximate Taylor theorem for analytic Lipschitz functions 解析 Lipschitz 函数的近似泰勒定理
arXiv - MATH - Functional Analysis Pub Date : 2024-08-05 DOI: arxiv-2408.02522
Stephen Deterding
{"title":"Approximate Taylor theorem for analytic Lipschitz functions","authors":"Stephen Deterding","doi":"arxiv-2408.02522","DOIUrl":"https://doi.org/arxiv-2408.02522","url":null,"abstract":"Let $U$ be a bounded open subset of the complex plane and let $A_{alpha}(U)$\u0000denote the set of functions analytic on $U$ that also belong to the little\u0000Lipschitz class with Lipschitz exponent $alpha$. It is shown that if\u0000$A_{alpha}(U)$ admits a bounded point derivation at $x in partial U$, then\u0000there is an approximate Taylor Theorem for $A_{alpha}(U)$ at $x$. This extends\u0000and generalizes known results concerning bounded point derivations.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"193 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930487","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}
引用次数: 0
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