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Larger greedy sums for reverse partially greedy bases 反向部分贪婪基的更大贪婪总和
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-28 DOI: 10.1007/s10476-024-00008-x
H. V. Chu
{"title":"Larger greedy sums for reverse partially greedy bases","authors":"H. V. Chu","doi":"10.1007/s10476-024-00008-x","DOIUrl":"10.1007/s10476-024-00008-x","url":null,"abstract":"<div><p>An interesting result due to Dilworth et al. was that if we enlarge\u0000greedy sums by a constant factor <span>(lambda &gt; 1)</span> in the condition defining the greedy\u0000property, then we obtain an equivalence of the almost greedy property, a strictly\u0000weaker property. Previously, the author showed that enlarging greedy sums by <span>(lambda)</span>\u0000in the condition defining the partially greedy (PG) property also strictly weakens\u0000the property. However, enlarging greedy sums in the definition of reverse partially\u0000greedy (RPG) bases by Dilworth and Khurana again gives RPG bases. The companion\u0000of PG and RPG bases suggests the existence of a characterization of RPG\u0000bases which, when greedy sums are enlarged, gives an analog of a result that holds\u0000for partially greedy bases. In this paper, we show that such a characterization\u0000indeed exists, answering positively a question previously posed by the author.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 1","pages":"111 - 125"},"PeriodicalIF":0.6,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323112","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
Sun Dual Theory For Bi-Continuous Semigroups 双连续半群的太阳二元论
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-28 DOI: 10.1007/s10476-024-00014-z
K. Kruse, F.L. Schwenninger
{"title":"Sun Dual Theory For Bi-Continuous Semigroups","authors":"K. Kruse,&nbsp;F.L. Schwenninger","doi":"10.1007/s10476-024-00014-z","DOIUrl":"10.1007/s10476-024-00014-z","url":null,"abstract":"<div><p> The sun dual space corresponding to a strongly continuous semigroup is a known concept when dealing with dual semigroups, which are in general only weak \u0000<span>(^*)</span>-continuous. In this paper we develop a corresponding theory for bi-continuous semigroups under mild assumptions on the involved locally convex topologies. We also discuss sun reflexivity and Favard spaces in this context, extending classical results by van Neerven. \u0000</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 1","pages":"235 - 280"},"PeriodicalIF":0.6,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-024-00014-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323092","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
Global Stein theorem on Hardy spaces 哈代空间上的全局斯坦因定理
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-22 DOI: 10.1007/s10476-024-00003-2
A. Bonami, S. Grellier, B. F. Sehba
{"title":"Global Stein theorem on Hardy spaces","authors":"A. Bonami,&nbsp;S. Grellier,&nbsp;B. F. Sehba","doi":"10.1007/s10476-024-00003-2","DOIUrl":"10.1007/s10476-024-00003-2","url":null,"abstract":"<div><p>Let <span>(f)</span> be an integrable function which has integral <span>(0)</span> on <span>(mathbb{R}^n )</span>.\u0000What is the largest condition on <span>(|f|)</span> that guarantees that <span>(f)</span> is in the Hardy space\u0000<span>(mathcal{H}^1(mathbb{R}^n))</span>? When <span>(f)</span> is compactly supported, it is well-known that the largest condition\u0000on <span>(|f|)</span> is the fact that <span>(|f|in L log L(mathbb{R}^n) )</span>. We consider the same kind of\u0000problem here, but without any condition on the support. We do so for <span>(mathcal{H}^1(mathbb{R}^n))</span>,\u0000as well as for the Hardy space <span>(mathcal{H}_{log}(mathbb{R}^n))</span> which appears in the study of pointwise\u0000products of functions in <span>(mathcal{H}^1(mathbb{R}^n))</span> and in its dual BMO.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 1","pages":"79 - 99"},"PeriodicalIF":0.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197506","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
Relationships between inessential, strictly singular, strictly cosingular and improjective linear relations 无本质线性关系、严格单线性关系、严格双线性关系和即兴线性关系之间的关系
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-03-22 DOI: 10.1007/s10476-024-00007-y
T. Álvarez, S. Keskes
{"title":"Relationships between inessential, strictly singular, strictly cosingular and improjective linear relations","authors":"T. Álvarez,&nbsp;S. Keskes","doi":"10.1007/s10476-024-00007-y","DOIUrl":"10.1007/s10476-024-00007-y","url":null,"abstract":"<div><p>This paper is devoted to study the interrelations between inessential, improjective, strictly singular and strictly cosingular linear relations. First, we show that the classes of strictly singular and strictly cosingular linear relations with finite dimensional multivalued part are contained in the class of inessential linear relations and that for many Banach spaces these inclusions are equalities. Moreover, we prove that the class of improjective linear relations contains the class of inessential linear relations and we also see that for the most classical Banach spaces the improjective linear relations with finite dimensional multivalued part coincide with the inessential linear relations with finite dimensional multivalued part. Finally, to give value to our results we construct an example of a closed everywhere defined linear relation with finite dimensional multivalued part of each of the following types: inessential not strictly singular. inessential not strictly cosingular. improjective not inessential.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 1","pages":"1 - 30"},"PeriodicalIF":0.6,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197287","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
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":"50 1","pages":"323 - 334"},"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":"50 1","pages":"281 - 294"},"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":"50 1","pages":"149 - 187"},"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":"50 1","pages":"215 - 233"},"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":"50 1","pages":"31 - 78"},"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":"50 1","pages":"189 - 213"},"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
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