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Fractional Orlicz-Sobolev embeddings
arXiv: Functional Analysis Pub Date : 2020-01-15 DOI: 10.1016/j.matpur.2020.12.007
A. Alberico, A. Cianchi, L. Pick, Lenka Slav'ikov'a
{"title":"Fractional Orlicz-Sobolev embeddings","authors":"A. Alberico, A. Cianchi, L. Pick, Lenka Slav'ikov'a","doi":"10.1016/j.matpur.2020.12.007","DOIUrl":"https://doi.org/10.1016/j.matpur.2020.12.007","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86240902","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: 38
A Weyl pseudodifferential calculus associated with exponential weights on Rd 与Rd上指数权重相关的Weyl伪微分演算
arXiv: Functional Analysis Pub Date : 2020-01-14 DOI: 10.1215/00192082-8886959
Sean Harris
{"title":"A Weyl pseudodifferential calculus associated with exponential weights on Rd","authors":"Sean Harris","doi":"10.1215/00192082-8886959","DOIUrl":"https://doi.org/10.1215/00192082-8886959","url":null,"abstract":"We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted $L^p$ spaces over $mathbb{R}^d$ with weights of the form $exp(-phi(x))$, for $phi$ a $C^2$ function, a setting in which the operator associated to the weighted Dirichlet form typically has only holomorphic functional calculus. A symbol class giving rise to bounded operators on $L^p$ is determined, and its properties analysed. This theory is used to calculate an upper bounded on the $H^infty$ angle of relevant operators, and deduces known optimal results in some cases. Finally, the symbol class is enriched and studied under an algebraic viewpoint.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83422232","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
Klein's Trace Inequality and Superquadratic Trace Functions 克莱因迹不等式与超二次迹函数
arXiv: Functional Analysis Pub Date : 2020-01-12 DOI: 10.20944/preprints201912.0192.v2
M. Kian, M. Alomari
{"title":"Klein's Trace Inequality and Superquadratic Trace Functions","authors":"M. Kian, M. Alomari","doi":"10.20944/preprints201912.0192.v2","DOIUrl":"https://doi.org/10.20944/preprints201912.0192.v2","url":null,"abstract":"We show that if $f$ is a non-negative superquadratic function, then $Amapstomathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, begin{align*} tr fleft( {frac{{A + B}}{2}} right) +tr fleft(left| {frac{{A - B}}{2}}right|right) leq frac{{tr {fleft( A right)} + tr {fleft( B right)} }}{2} end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]geq mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72673970","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: 1
Szegő-type limit theorems for "multiplicative Toeplitz" operators and non-Følner approximations Szegő-type“乘法Toeplitz”算子和非f ølner近似的极限定理
arXiv: Functional Analysis Pub Date : 2020-01-06 DOI: 10.1090/SPMJ/1683
N. Nikolski, A. Pushnitski
{"title":"Szegő-type limit theorems for \"multiplicative Toeplitz\" operators and non-Følner approximations","authors":"N. Nikolski, A. Pushnitski","doi":"10.1090/SPMJ/1683","DOIUrl":"https://doi.org/10.1090/SPMJ/1683","url":null,"abstract":"We discuss an analogue of the First Szegő Limit Theorem for multiplicative Toeplitz operators and highlight the role of the multliplicative Folner condition in this topic.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79400205","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: 4
On Arens regularity of projective tensor product of Schatten spaces Schatten空间射影张量积的Arens正则性
arXiv: Functional Analysis Pub Date : 2020-01-02 DOI: 10.1216/rmj.2021.51.1433
L. Singh
{"title":"On Arens regularity of projective tensor product of Schatten spaces","authors":"L. Singh","doi":"10.1216/rmj.2021.51.1433","DOIUrl":"https://doi.org/10.1216/rmj.2021.51.1433","url":null,"abstract":"In this paper we discuss the Arens regularity of projective tensor product of Schatten p-class operators. We use the biregularity condition given by \"Ulger to prove that $S_p(mathcal H)otimes^gamma S_q(mathcal H)$ is not Arens regular. We further prove that $B(S_2(mathcal H))otimes^gamma S_2(mathcal H)$ is not Arens regular(with respect to usual multiplication) while it is regular with respect to Schur product. Thus we demonstrate the importance of biregularity condition given in cite{Ulger} and the convenience of its use to prove Arens regularity or irregularity through some concrete examples.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77199078","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: 1
Conducting standard functional analysis sessions 进行标准的功能分析
arXiv: Functional Analysis Pub Date : 2020-01-01 DOI: 10.1016/b978-0-12-817212-4.00002-x
J. Chok, Jill M. Harper, M. Weiss, F. Bird, J. Luiselli
{"title":"Conducting standard functional analysis sessions","authors":"J. Chok, Jill M. Harper, M. Weiss, F. Bird, J. Luiselli","doi":"10.1016/b978-0-12-817212-4.00002-x","DOIUrl":"https://doi.org/10.1016/b978-0-12-817212-4.00002-x","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84210944","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
Copyright 版权
arXiv: Functional Analysis Pub Date : 2020-01-01 DOI: 10.1016/b978-0-12-817212-4.00009-2
{"title":"Copyright","authors":"","doi":"10.1016/b978-0-12-817212-4.00009-2","DOIUrl":"https://doi.org/10.1016/b978-0-12-817212-4.00009-2","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76903316","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
Gelfand Triples for the Kohn–Nirenberg Quantization on Homogeneous Lie Groups 齐次李群上Kohn-Nirenberg量化的Gelfand三元组
arXiv: Functional Analysis Pub Date : 2020-01-01 DOI: 10.1007/978-3-030-58215-9_3
Jonas Brinker, J. Wirth
{"title":"Gelfand Triples for the Kohn–Nirenberg Quantization on Homogeneous Lie Groups","authors":"Jonas Brinker, J. Wirth","doi":"10.1007/978-3-030-58215-9_3","DOIUrl":"https://doi.org/10.1007/978-3-030-58215-9_3","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86651802","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
Front-matter 前页
arXiv: Functional Analysis Pub Date : 2020-01-01 DOI: 10.1016/b978-0-12-817212-4.00008-0
{"title":"Front-matter","authors":"","doi":"10.1016/b978-0-12-817212-4.00008-0","DOIUrl":"https://doi.org/10.1016/b978-0-12-817212-4.00008-0","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81898936","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
Series foreword: Critical specialties in treating autism and other behavioral challenges 系列前言:治疗自闭症和其他行为挑战的关键专业
arXiv: Functional Analysis Pub Date : 2020-01-01 DOI: 10.1016/b978-0-12-817212-4.00012-2
{"title":"Series foreword: Critical specialties in treating autism and other behavioral challenges","authors":"","doi":"10.1016/b978-0-12-817212-4.00012-2","DOIUrl":"https://doi.org/10.1016/b978-0-12-817212-4.00012-2","url":null,"abstract":"","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79156731","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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