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Evaluations of sums involving odd harmonic numbers and binomial coefficients 涉及奇次谐波数和二项式系数的和的求值
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-22 DOI: 10.1007/s10476-024-00011-2
W. Zheng, Y. Yang
{"title":"Evaluations of sums involving odd harmonic numbers and binomial coefficients","authors":"W. Zheng,&nbsp;Y. Yang","doi":"10.1007/s10476-024-00011-2","DOIUrl":"10.1007/s10476-024-00011-2","url":null,"abstract":"<div><p>In this paper, we extend tools developed in [9] to study Euler <i>T</i>-type sums involving odd harmonic numbers and binomial coefficients. In particular, we will prove that two kinds of Euler <i>T</i>-type sums can be expressed in terms of log(2), zeta values, double <i>T</i>-values, (odd) harmonic numbers and double <i>T</i>-sums.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197429","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
Weighted weak type mixed (Phi)-inequalities for martingale maximal operator 马丁格尔最大算子的加权弱型混合 $$Phi$ -inequalities
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-22 DOI: 10.1007/s10476-024-00005-0
Y. Ren
{"title":"Weighted weak type mixed (Phi)-inequalities for martingale maximal operator","authors":"Y. Ren","doi":"10.1007/s10476-024-00005-0","DOIUrl":"10.1007/s10476-024-00005-0","url":null,"abstract":"<div><p>In this article, some necessary and sufficient conditions are\u0000shown for weighted weak type mixed <span>(Phi)</span>-inequality and weighted extra-weak type\u0000mixed <span>(Phi)</span>-inequality for martingale maximal operator. The obtained results generalize\u0000some existing statements.\u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197089","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 coexistence of convergence and divergence phenomena for integral averages and an application to the Fourier–Haar series 论积分平均数的收敛与发散现象并存以及在傅立叶-哈尔数列中的应用
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-22 DOI: 10.1007/s10476-024-00010-3
M. Hirayama, D. Karagulyan
{"title":"On the coexistence of convergence and divergence phenomena for integral averages and an application to the Fourier–Haar series","authors":"M. Hirayama,&nbsp;D. Karagulyan","doi":"10.1007/s10476-024-00010-3","DOIUrl":"10.1007/s10476-024-00010-3","url":null,"abstract":"<div><p>Let <span>(C,Dsubset mathbb{N})</span> be disjoint sets, and <span>(mathcal{C}={1/2^{c}colon cin C}, mathcal{D}={1/2^{d}colon din D})</span>. \u0000We consider the associate bases of dyadic, axis-parallel rectangles <span>(mathcal{R}_{mathcal{C}})</span> and <span>(mathcal{R}_{mathcal{D}})</span>. \u0000We give necessary and sufficient conditions on the sets <span>(mathcal{C} and mathcal{D})</span> such that there is a positive function <span>(fin L^{1}([0,1)^{2}))</span> so that the integral averages are convergent with respect to <span>(mathcal{R}_{mathcal{C}})</span> and divergent for <span>(mathcal{R}_{mathcal{D}})</span>. \u0000We next apply our results to the two-dimensional Fourier--Haar series and characterize convergent and divergent sub-indices. \u0000The proof is based on some constructions from the theory of low-discrepancy sequences such as the van der Corput sequence and an associated tiling of the unit square.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197175","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
Weighted boundary limits of the Kobayashi--Fuks metric on h-extendible domains 可扩展域上小林--福克斯度量的加权边界极限
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-19 DOI: 10.1007/s10476-024-00013-0
Debaprasanna Kar
{"title":"Weighted boundary limits of the Kobayashi--Fuks metric on h-extendible domains","authors":"Debaprasanna Kar","doi":"10.1007/s10476-024-00013-0","DOIUrl":"10.1007/s10476-024-00013-0","url":null,"abstract":"<div><p>We study the boundary behavior of the Kobayashi--Fuks metric on the class of h-extendible domains. Here, we derive the nontangential boundary asymptotics of the Kobayashi--Fuks metric and its Riemannian volume element by the help of some maximal domain functions and then using their stability results on h-extendible local models.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168529","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
Duality for vector-valued Bergman–Orlicz spaces and little Hankel operators between vector-valued Bergman–Orlicz spaces on the unit ball 单位球上的矢量值伯格曼-奥立兹空间和矢量值伯格曼-奥立兹空间之间的小汉克尔算子的对偶性
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s10476-024-00002-3
D. Békollè, T. Mfouapon, E. L. Tchoundja
{"title":"Duality for vector-valued Bergman–Orlicz spaces and little Hankel operators between vector-valued Bergman–Orlicz spaces on the unit ball","authors":"D. Békollè,&nbsp;T. Mfouapon,&nbsp;E. L. Tchoundja","doi":"10.1007/s10476-024-00002-3","DOIUrl":"10.1007/s10476-024-00002-3","url":null,"abstract":"<div><p>In this paper, we consider vector-valued Bergman–Orlicz spaces which are generalization of classical vector-valued Bergman spaces. We characterize the dual space of vector-valued Bergman–Orlicz space, and study the boundedness of the little Hankel operators, \u0000<span>(h_b)</span>, with operator-valued symbols <i>b</i>, between different weighted vector-valued Bergman–Orlicz spaces on the unit ball <span>(mathbb{B}_n)</span>.More precisely, given two complex Banach spaces <i>X</i>, <i>Y</i>, we characterize those operator-valued symbols<span>(b colon mathbb{B}_nrightarrow mathcal{L} (overline{X},Y) )</span> for which the little Hankel operator <span>(h_{b}: A^{Phi_{1}}_{alpha}(mathbb{B}_{n},X) longrightarrow A^{Phi_{2}}_{alpha}(mathbb{B}_{n},Y))</span>, extends into a bounded operator, where <span>(Phi_{1})</span> and <span>(Phi_2)</span> are either convex or concave growth functions.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140116890","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
Nonstationary matrix-valued multiresolution analysis from the extended affine group 来自扩展仿射组的非稳态矩阵值多分辨率分析
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-02-26 DOI: 10.1007/s10476-024-00004-1
D. Jindal, L. K. Vashisht
{"title":"Nonstationary matrix-valued multiresolution analysis from the extended affine group","authors":"D. Jindal,&nbsp;L. K. Vashisht","doi":"10.1007/s10476-024-00004-1","DOIUrl":"10.1007/s10476-024-00004-1","url":null,"abstract":"<div><p>We characterize scaling functions of nonstationary matrix-valued\u0000multiresolution analysis in the matrix-valued function space <span>(L^2(mathbb{R}, mathbb{C}^{l times l}))</span>, l is a natural\u0000number. This is inspired by the work of Novikov, Protasov and Skopina on\u0000nonstationary multiresolution analysis of the space <span>(L^2(mathbb{R}))</span>. Using a sequence of diagonal\u0000matrix-valued scaling functions in <span>(L^2(mathbb{R}, mathbb{C}^{l times l}))</span>, the construction of matrixvalued\u0000nonstationary orthonormal wavelets associated with the affine group is\u0000presented. Nonstationary matrix-valued wavelet frames in terms of frames of\u0000closed subspaces associated with a given nonstationary multiresolution analysis\u0000are given. Finally, we give sufficient conditions for the sequence of scaling functions\u0000of nonstationary matrix-valued multiresolution analysis in the frequency\u0000domain.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979691","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
Reaction-diffusion equations on metric graphs with edge noise 有边缘噪声的度量图上的反应扩散方程
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-02-20 DOI: 10.1007/s10476-024-00006-z
E. Sikolya
{"title":"Reaction-diffusion equations on metric graphs with edge noise","authors":"E. Sikolya","doi":"10.1007/s10476-024-00006-z","DOIUrl":"10.1007/s10476-024-00006-z","url":null,"abstract":"<div><p>We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in \u0000[14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from \u0000[15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. </p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00006-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139925522","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
Quasilinear PDEs, Interpolation Spaces and Hölderian mappings 拟线性偏微分方程，插值空间和Hölderian映射
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-11-15 DOI: 10.1007/s10476-023-0245-z
I. Ahmed, A. Fiorenza, M. R. Formica, A. Gogatishvili, A. El Hamidi, J. M. Rakotoson
{"title":"Quasilinear PDEs, Interpolation Spaces and Hölderian mappings","authors":"I. Ahmed,&nbsp;A. Fiorenza,&nbsp;M. R. Formica,&nbsp;A. Gogatishvili,&nbsp;A. El Hamidi,&nbsp;J. M. Rakotoson","doi":"10.1007/s10476-023-0245-z","DOIUrl":"10.1007/s10476-023-0245-z","url":null,"abstract":"<div><p>As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of <i>α</i>-Hölderian mappings between normed spaces, by studying the action of the mappings on <i>K</i>-functionals and between interpolation spaces with logarithm functions. We apply these results to obtain some regularity results on the gradient of the solutions to quasilinear equations of the form </p><div><div><span>$$-text{div}(widehat{a}(nabla u))+V(u)=f,$$</span></div></div><p> where <i>V</i> is a nonlinear potential and <i>f</i> belongs to non-standard spaces like Lorentz–Zygmund spaces. We show several results; for instance, that the mapping <span>(cal{T}:cal{T}f=nabla u)</span> is locally or globally <i>α</i>-Hölderian under suitable values of <i>α</i> and appropriate hypotheses on <i>V</i> and <i>â</i>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796394","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
Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative Besov空间、Schatten类和量化导数的加权形式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-11-15 DOI: 10.1007/s10476-023-0246-y
Z. Gong, J. Li, B. D. Wick
{"title":"Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative","authors":"Z. Gong,&nbsp;J. Li,&nbsp;B. D. Wick","doi":"10.1007/s10476-023-0246-y","DOIUrl":"10.1007/s10476-023-0246-y","url":null,"abstract":"<div><p>In this paper, we establish the Schatten class and endpoint weak Schatten class estimates for the commutator of Riesz transforms on weighted <i>L</i><sup>2</sup> spaces. As an application a weighted version for the estimate of the quantised derivative introduced by Alain Connes and studied recently by Lord–McDonald–Sukochev–Zanin and Frank–Sukochev–Zanin is provided.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0246-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796398","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
Preface to this Special Issue Dedicated to Oleg V. Besov 本特刊献给奥列格·v·别索夫的序言
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-11-15 DOI: 10.1007/s10476-023-0244-0
Vladimir D. Stepanov
{"title":"Preface to this Special Issue Dedicated to Oleg V. Besov","authors":"Vladimir D. Stepanov","doi":"10.1007/s10476-023-0244-0","DOIUrl":"10.1007/s10476-023-0244-0","url":null,"abstract":"","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796393","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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