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Wavelet series expansion in Hardy spaces with approximate duals 具有近似对偶的哈代空间中的小波级数展开
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-05-13 DOI: 10.1007/s10476-024-00022-z
Y. Hur, H. Lim
{"title":"Wavelet series expansion in Hardy spaces with approximate duals","authors":"Y. Hur,&nbsp;H. Lim","doi":"10.1007/s10476-024-00022-z","DOIUrl":"10.1007/s10476-024-00022-z","url":null,"abstract":"<div><p>In this paper, we provide sufficient conditions for the functions \u0000<span>( psi )</span> and <span>( phi )</span> to be the approximate duals in the Hardy space <span>(H^p(mathbb{R}))</span> for all <span>( 0&lt;ple 1 )</span>.\u0000Based on these conditions, we obtain the wavelet series expansion in the Hardy\u0000space <span>(H^p(mathbb{R}))</span> with the approximate duals. The important properties of our approach\u0000include the following: (i) our results work for any <span>( 0&lt;p leq 1 )</span>; (ii) we do not\u0000assume that the functions <span>( psi )</span> and <span>( phi )</span> are exact duals; (iii) we provide a tractable\u0000bound for the operator norm of the associated wavelet frame operator so that it\u0000is possible to check the suitability of the functions <span>( psi )</span> and <span>( phi )</span>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"563 - 595"},"PeriodicalIF":0.6,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941945","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
Composition operators on variable exponent Lebesgue spaces 可变指数勒贝格空间上的合成算子
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-04-30 DOI: 10.1007/s10476-024-00015-y
D. S. Bajaj, G. Datt
{"title":"Composition operators on variable exponent Lebesgue spaces","authors":"D. S. Bajaj,&nbsp;G. Datt","doi":"10.1007/s10476-024-00015-y","DOIUrl":"10.1007/s10476-024-00015-y","url":null,"abstract":"<div><p>We study composition operators between variable exponent\u0000Lebesgue spaces and characterize boundedness and compactness of the composition operators on a variable exponent Lebesgue space. We also derive a sufficient condition for composition operator to have a closed range and explain some\u0000properties which these operators share with the case of Lebesgue spaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"345 - 366"},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140836968","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
m-pseudoconcavity and compactness 米伪腔和紧凑性
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-04-30 DOI: 10.1007/s10476-024-00017-w
O. Günyüz
{"title":"m-pseudoconcavity and compactness","authors":"O. Günyüz","doi":"10.1007/s10476-024-00017-w","DOIUrl":"10.1007/s10476-024-00017-w","url":null,"abstract":"<div><p>The core of a compact set in a general complex manifold has been\u0000defined by Shcherbina very recently to study the existence of strictly plurisubharmonic functions on compact sets. In this paper, using <i>m</i>-subharmonic functions\u0000on compact subsets of a non-compact Kähler manifold, we define the set <i>m</i>-core\u0000of a compact set and investigate the structure of it.</p><p>\u0000We will have the decomposition of the m-minimal kernel of a weakly\u0000<i>m</i>-complete manifold and show that it can be fully decomposed into compact\u0000<i>m</i>-pseudoconcave subsets via certain results obtained in the author’s very recent\u0000papers to have the disintegration of the set <i>m</i>-core of the entire Kähler manifold\u0000(or of a domain in the manifold) and to study the characterization of so-called\u0000<i>m</i>-Stein manifolds.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"537 - 551"},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140836959","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 functions of bounded mean oscillation with bounded negative part 关于具有有界负部分的有界平均振荡函数
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-04-30 DOI: 10.1007/s10476-024-00018-9
H. Zhao, D. Wang
{"title":"On functions of bounded mean oscillation with bounded negative part","authors":"H. Zhao,&nbsp;D. Wang","doi":"10.1007/s10476-024-00018-9","DOIUrl":"10.1007/s10476-024-00018-9","url":null,"abstract":"<div><p>Let <span>(b)</span> be a locally integrable function and <span>(mathfrak{M})</span> be the bilinear maximal function\u0000</p><div><div><span>$$mathfrak{M}(f,g)(x)=sup_{Qni x}frac{1}{|Q|}int_{Q}|f(y)g(2x-y)|dy.$$</span></div></div><p>\u0000In this paper, characterization of the BMO function in terms of commutator <span>(mathfrak{M}^{(1)}_{b})</span> is established. Also, we obtain the necessary and sufficient conditions for the boundedness of the commutator <span>([b, mathfrak{M}]_{1})</span>. Moreover, some new characterizations of Lipschitz and non-negative Lipschitz functions are obtained.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 2","pages":"717 - 730"},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140837125","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
Trigonometric series and the permutation sign convergence condition 三角级数和包络符号收敛条件
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-04-08 DOI: 10.1007/s10476-024-00012-1
G. Chelidze, S. Chobanyan, G. Giorgobiani, V. Tarieladze
{"title":"Trigonometric series and the permutation sign convergence condition","authors":"G. Chelidze,&nbsp;S. Chobanyan,&nbsp;G. Giorgobiani,&nbsp;V. Tarieladze","doi":"10.1007/s10476-024-00012-1","DOIUrl":"10.1007/s10476-024-00012-1","url":null,"abstract":"<div><p>We prove that a uniformly convergent trigonometric series may not satisfy the permutation sign convergence condition, hence it may not satisfy the Rademacher condition as well.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 1","pages":"101 - 110"},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587462","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
Observations on some classes of operators on C(K,X) 关于 C(K,X) 上某些类算子的观察结果
IF 0.6 3区 数学
Analysis Mathematica Pub Date : 2024-04-02 DOI: 10.1007/s10476-024-00009-w
I. Ghenciu, R. Popescu
{"title":"Observations on some classes of operators on C(K,X)","authors":"I. Ghenciu,&nbsp;R. Popescu","doi":"10.1007/s10476-024-00009-w","DOIUrl":"10.1007/s10476-024-00009-w","url":null,"abstract":"<div><p>Suppose <i>X</i> and <i>Y</i> are Banach spaces, <i>K</i> is a compact Hausdorff space, <span>(Sigma)</span> is the <span>(sigma)</span>-algebra of Borel subsets of <i>K</i>, <span>(C(K,X))</span> is the Banach space of all continuous <i>X</i>-valued functions (with the supremum norm), and <span>(T colon C(K,X)to Y)</span> is a strongly bounded operator with representing measure <span>(m colon Sigma to L(X,Y))</span>. \u0000We show that if <span>(hat{T} colon B(K, X) to Y)</span> is its extension, then <i>T</i> is weak Dunford--Pettis (resp.weak<sup>*</sup> Dunford--Pettis, weak <i>p</i>-convergent, weak<sup>*</sup> <i>p</i>-convergent) if and only if <span>(hat{T})</span> has the same property.</p><p>We prove that if <span>(T colon C(K,X)to Y)</span> is strongly bounded limited completely continuous (resp. limited <i>p</i>-convergent), then <span>(m(A) colon Xto Y)</span> is limited completely continuous (resp. limited <i>p</i>-convergent) for each <span>(Ain Sigma)</span>. We also prove that the above implications become equivalences when <i>K</i> is a dispersed compact Hausdorff space.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 1","pages":"127 - 148"},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587463","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
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
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