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On vector-valued functions with small Riemann sums 关于具有小黎曼和的向量值函数
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-03-12 DOI: 10.1007/s10476-026-00147-3
K. Naralenkov
{"title":"On vector-valued functions with small Riemann sums","authors":"K. Naralenkov","doi":"10.1007/s10476-026-00147-3","DOIUrl":"10.1007/s10476-026-00147-3","url":null,"abstract":"<div><p>We introduce various global smallness conditions for Riemann sums within the vector-valued Riemann-measurable function class. In terms of these conditions, we clarify to some extent the nature of the differences between the absolute Birkhoff, McShane and Henstock integrals from one side and the <span>A</span>-Riemann, <span>A</span>- and <span>Q</span>-integrals from the other side. In particular, we prove that the McShane and <span>A</span>-Riemann integrals do not contradict one another.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"277 - 289"},"PeriodicalIF":0.5,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665739","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}
引用次数: 0
EXTREME INEQUALITIES OF GENERAL (L_p) (mu)-PROJECTION BODY AND GENERAL (L_p) (mu)-CENTROID BODY 一般(L_p)(mu) -投影体和一般(L_p)(mu) -质心体的极端不等式
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-03-09 DOI: 10.1007/s10476-026-00144-6
C. Li, G. Chen
{"title":"EXTREME INEQUALITIES OF GENERAL (L_p) (mu)-PROJECTION BODY AND GENERAL (L_p) (mu)-CENTROID BODY","authors":"C. Li,&nbsp;G. Chen","doi":"10.1007/s10476-026-00144-6","DOIUrl":"10.1007/s10476-026-00144-6","url":null,"abstract":"<div><p>In this paper, we introduce the concept of general <span>(L_p)</span> projection body and general <span>(L_p)</span> centroid body of general measures with positive homogeneity density function, and prove the corresponding extreme inequalities. Meanwhile, we also study their measure comparison problems and monotone inequalities.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"179 - 207"},"PeriodicalIF":0.5,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665672","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}
引用次数: 0
Remark on the Cauchy-Schwarz inequality 关于Cauchy-Schwarz不等式的注解
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-03-04 DOI: 10.1007/s10476-026-00140-w
R. Kumar, M. Verma
{"title":"Remark on the Cauchy-Schwarz inequality","authors":"R. Kumar,&nbsp;M. Verma","doi":"10.1007/s10476-026-00140-w","DOIUrl":"10.1007/s10476-026-00140-w","url":null,"abstract":"<div><p>In this paper, we introduce a generalization and refinement of the Cauchy-Schwarz inequality within the framework of positive functionals. By employing elementary techniques, we sharpen the Cauchy-Schwarz inequality for real numbers, specifically for a particular class of unital positive functionals. Additionally, our results yield a variety of related inequalities, demonstrating the broader applicability of this approach.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"173 - 178"},"PeriodicalIF":0.5,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665728","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}
引用次数: 0
Stability of A(mathbb{T})-relations in (C^*)-algebras with tracial rank at most one 迹列最多为1的(C^*) -代数中A (mathbb{T}) -关系的稳定性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-24 DOI: 10.1007/s10476-026-00139-3
J. Hua
{"title":"Stability of A(mathbb{T})-relations in (C^*)-algebras with tracial rank at most one","authors":"J. Hua","doi":"10.1007/s10476-026-00139-3","DOIUrl":"10.1007/s10476-026-00139-3","url":null,"abstract":"<div><p>An old and famous problem from the 1950s, popularized by Halmos, is that whether any pair of almost commuting contractive self-adjoint matrices are norm close to a pair of exactly commuting self-adjoint matrices? This question was solved affirmatively by Lin in the 1990's. In this paper, we study the general Halmos problem concerning unitary elements in <span>(C^*)</span>-algebras. Specifically, we first introduce the definition of A<span>(mathbb{T})</span>-relations, and then we give a necessary and sufficient condition for the stability of A<span>(mathbb{T})</span>-relations in any unital infinite\u0000dimensional simple separable <span>(C^*)</span>-algebra with tracial rank at most one. Finally, as applications, we show that many naturally occurring relations are A<span>(mathbb{T})</span>-relations, and thus the stability results of these relations can be obtained by applying the above conclusions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"117 - 151"},"PeriodicalIF":0.5,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665677","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}
引用次数: 0
Optimality conditions for change of variable operators in Sobolev spaces with mixed derivatives 具有混合导数的Sobolev空间中变量算子变化的最优性条件
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-23 DOI: 10.1007/s10476-026-00141-9
V. K. Nguyen
{"title":"Optimality conditions for change of variable operators in Sobolev spaces with mixed derivatives","authors":"V. K. Nguyen","doi":"10.1007/s10476-026-00141-9","DOIUrl":"10.1007/s10476-026-00141-9","url":null,"abstract":"<div><p>Change of variable plays an important role in constructing sparse grids for multivariate numerical integration of functions on \u0000<span>([0,1]^d)</span>. This is a modification of \u0000cubature formulae for functions supported in <span>([0,1]^d)</span> \u0000which yields the same order of convergence. \u0000In this paper we prove the necessary and sufficient conditions for the continuity of the change of variable operator in the Sobolev space with \u0000mixed derivatives <span>(boldsymbol{W}_p^m (mathbb{R}^d))</span>\u0000 with <span>(1leq p&lt;infty)</span>\u0000 . The result is then extended to the spaces on the unit cube \u0000 <span>(boldsymbol{W}_p^m([0,1]^d))</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"291 - 306"},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665673","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}
引用次数: 0
A note on the conjugates of nuclear operators 关于核算子共轭的注释
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-23 DOI: 10.1007/s10476-026-00142-8
M. Nowak
{"title":"A note on the conjugates of nuclear operators","authors":"M. Nowak","doi":"10.1007/s10476-026-00142-8","DOIUrl":"10.1007/s10476-026-00142-8","url":null,"abstract":"<div><p>Let <span>((Omega,Sigma,mu))</span> be a finite measure space and <i>X</i> and <i>Y</i> be real Banach spaces. It is shown that if <span>(T colon L^infty(mu,X)rightarrow Y)</span> is a <span>(sigma )</span>-order continuous\u0000operator and <span>(X ^{*} )</span> has the Radon-Nikodym property, <i>Y</i> is reflexive, then <i>T</i>\u0000is a nuclear operator if and only if its conjugate operator\u0000<span>(T ^{*} :Y ^{*} rightarrow L^1(mu,X ^{*} ))</span> is nuclear. In this case, <span>(|T| _{rm nuc}=|T ^{*} | _{rm nuc})</span>.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"333 - 341"},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665737","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}
引用次数: 0
Calderón–Zygmund operators and commutators on weighted Hardy spaces Calderón-Zygmund加权Hardy空间上的算子和换向子
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-02-23 DOI: 10.1007/s10476-026-00138-4
Y. Han, F. Liu, H. Wu
{"title":"Calderón–Zygmund operators and commutators on weighted Hardy spaces","authors":"Y. Han,&nbsp;F. Liu,&nbsp;H. Wu","doi":"10.1007/s10476-026-00138-4","DOIUrl":"10.1007/s10476-026-00138-4","url":null,"abstract":"<div><p>Two classes of Hörmander type conditions are introduced in the present paper. These conditions are weaker strictly than the classical standard Calderón–Zygmund kernels. A systematical study is given for the bounds of the Calderón–Zygmund operator with the above Hörmander type kernels and their commutators on the weighted Hardy spaces. The main results of this paper essentially improve a large classes of classical works. It should be pointed out that the main results are new, even in the unweighted case.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"87 - 115"},"PeriodicalIF":0.5,"publicationDate":"2026-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665729","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}
引用次数: 0
On the local regularity of the Hilbert transform 希尔伯特变换的局部正则性
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-01-26 DOI: 10.1007/s10476-025-00137-x
Y. Pan, J. Wang, Y. Yan
{"title":"On the local regularity of the Hilbert transform","authors":"Y. Pan,&nbsp;J. Wang,&nbsp;Y. Yan","doi":"10.1007/s10476-025-00137-x","DOIUrl":"10.1007/s10476-025-00137-x","url":null,"abstract":"<div><p>In this paper the local regularity of the Hilbert transform is studied, and local smoothness and real analyticity results are obtained.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"343 - 374"},"PeriodicalIF":0.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-025-00137-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds and asymptotic expansions for the radii of convexity and uniform convexity of normalized Bessel functions 归一化贝塞尔函数的凸半径和一致凸半径的界和渐近展开式
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2026-01-14 DOI: 10.1007/s10476-025-00136-y
Á. Baricz, P. Kumar, S. Singh
{"title":"Bounds and asymptotic expansions for the radii of convexity and uniform convexity of normalized Bessel functions","authors":"Á. Baricz,&nbsp;P. Kumar,&nbsp;S. Singh","doi":"10.1007/s10476-025-00136-y","DOIUrl":"10.1007/s10476-025-00136-y","url":null,"abstract":"<div><p>This paper explores the asymptotic behavior of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence relations for the associated coefficients. Additionally, we derive generalized bounds for the radii of convexity and uniform convexity by applying the Euler–Rayleigh inequality and potential polynomials. The asymptotic inversion method and Rayleigh sums are the main tools used in the proofs.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"52 1","pages":"1 - 43"},"PeriodicalIF":0.5,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665736","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}
引用次数: 0
Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality 由Barthe的逆Brascamp-Lieb不等式证明Liakopoulos广义对偶Loomis-Whitney不等式中的等式
IF 0.5 3区 数学
Analysis Mathematica Pub Date : 2025-11-27 DOI: 10.1007/s10476-025-00134-0
K. J. Böröczky, F. Fodor, P. Kalantzopoulos
{"title":"Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality","authors":"K. J. Böröczky,&nbsp;F. Fodor,&nbsp;P. Kalantzopoulos","doi":"10.1007/s10476-025-00134-0","DOIUrl":"10.1007/s10476-025-00134-0","url":null,"abstract":"<div><p>We use the characterization of the case of equality in Barthe's geometric reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sections by certain lower-dimensional linear subspaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"51 4","pages":"1229 - 1245"},"PeriodicalIF":0.5,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766276","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}
引用次数: 0
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