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On the Commutativity of Closed Symmetric Operators 关于闭对称算子的交换性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0226-2
S. Dehimi, M. H. Mortad, A. Bachir
{"title":"On the Commutativity of Closed Symmetric Operators","authors":"S. Dehimi,&nbsp;M. H. Mortad,&nbsp;A. Bachir","doi":"10.1007/s10476-023-0226-2","DOIUrl":"10.1007/s10476-023-0226-2","url":null,"abstract":"<div><p>In this paper, we mainly show that if a product <i>AB</i> (or <i>BA</i>) of a closed symmetric operator <i>A</i> and a bounded positive operator <i>B</i> is normal, then it is self-adjoint. Equivalently, this means that <i>B</i> commutes with <i>A</i>. Certain generalizations and consequences are also presented.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43472144","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 Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators 关于与Schrödinger算子相关的换向子振荡和变分的加权紧性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0229-z
A. Ge, Q. He, D. Yan
{"title":"On Weighted Compactness of Oscillation and Variation of Commutators Associated with Schrödinger Operators","authors":"A. Ge,&nbsp;Q. He,&nbsp;D. Yan","doi":"10.1007/s10476-023-0229-z","DOIUrl":"10.1007/s10476-023-0229-z","url":null,"abstract":"<div><p>Let <span>({cal L} = - Delta + V)</span> be a Schrödinger operator with a nonnegative potential <i>V</i> belonging to the reverse Hölder class <i>B</i><sub><i>q</i></sub> for <i>q</i>&gt; <i>n</i>/2. In this paper, we study the weighted compactness of oscillation and variation commutators generated by BMO-type functions and some Schrödinger operators, which include Riesz transform and other standard Calderón–Zygmund operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0229-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41861009","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
On Meromorphic Solutions of Nonlinear Complex Differential Equations 关于非线性复微分方程的亚纯解
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0225-3
J.-F. Chen, Y.-Y. Feng
{"title":"On Meromorphic Solutions of Nonlinear Complex Differential Equations","authors":"J.-F. Chen,&nbsp;Y.-Y. Feng","doi":"10.1007/s10476-023-0225-3","DOIUrl":"10.1007/s10476-023-0225-3","url":null,"abstract":"<div><p>By utilizing Nevanlinna theory of meromorphic functions, we characterize meromorphic solutions of the following nonlinear differential equation of the form </p><div><div><span>$${f^n}{f^prime } + P(z,f,{f^prime }, ldots ,{f^{(t)}}) = {P_1}{e^{{alpha _1}z}} + {P_2}{e^{{alpha _2}z}} + cdots + {P_m}{e^{{alpha _m}z}},$$</span></div></div><p> where <i>n</i> ≥ 3, <i>t</i> ≥ 0 and <i>m</i> ≥ 1 are integers, <i>n</i> ≥ <i>m, P</i>(<i>z, f, f′, …, f</i><sup>(<i>t</i>)</sup>) is a differential polynomial in <i>f</i> (<i>z</i>) of degree <i>d</i> ≤ <i>n</i> with small functions of <i>f</i> (<i>z</i>) as its coefficients, and α<sub><i>j</i></sub>, <i>P</i><sub><i>j</i></sub> (<i>j</i> = 1, 2, …, <i>m</i>) are nonzero constants such that ∣α<sub>1</sub>∣ &gt; ∣α<sub>2</sub>∣ &gt; … &gt; ∣α<sub><i>m</i></sub>∣. Also we provide the concrete forms of the solutions of the equation above, and present some examples illustrating the sharpness of our results.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0225-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41583690","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
Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G) 群代数上某些Banach右模的射影性ℓ1（G）
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0234-2
S. Soltani Renani, Z. Yari
{"title":"Projectivity of Some Banach Right Modules over the Group Algebra ℓ1(G)","authors":"S. Soltani Renani,&nbsp;Z. Yari","doi":"10.1007/s10476-023-0234-2","DOIUrl":"10.1007/s10476-023-0234-2","url":null,"abstract":"<div><p>Let <i>G</i> be a locally compact group, <span>({cal B}({L^2}(G)))</span> be the space of all bounded linear operators on <i>L</i><sup>2</sup>(<i>G</i>), and <span>(({cal T}({L^2}(G)), ast))</span> be the Banach algebra of trace class operators on <i>L</i><sup>2</sup>(<i>G</i>). In this paper, we focus on some Banach right submodules of <span>({cal B}({L^2}(G)))</span> over the convolution algebras <span>(({cal T}({L^2}(G)), ast))</span> and (<i>L</i><sup>1</sup>(<i>G</i>),*). We will see that if the locally compact group <i>G</i> is discrete, then the Banach right <i>ℓ</i><sup>1</sup>(<i>G</i>)-module structures of them are derived from their Banach right <span>({cal T}({ell ^2}(G)))</span>-module structures. We also study the projectivity of these Banach right <i>ℓ</i><sup>1</sup>(<i>G</i>)-modules.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46322216","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
Completion Procedures in Measure Theory 测量理论中的完成程序
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0233-3
A. G. Smirnov, M. S. Smirnov
{"title":"Completion Procedures in Measure Theory","authors":"A. G. Smirnov,&nbsp;M. S. Smirnov","doi":"10.1007/s10476-023-0233-3","DOIUrl":"10.1007/s10476-023-0233-3","url":null,"abstract":"<div><p>We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content <i>μ</i>. With every such ring <span>({cal N})</span>, an extension of <i>μ</i> is naturally associated which is called the <span>({cal N})</span>-completion of <i>μ</i>. The <span>({cal N})</span>-completion operation comprises most previously known completion-type procedures and also gives rise to some new extensions, which may be useful for constructing counterexamples in measure theory. We find a condition ensuring that <i>σ</i>-additivity of a content is preserved under the <span>({cal N})</span>-completion and establish a criterion for the <span>({cal N})</span>-completion of a measure to be again a measure.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42483533","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 ({cal A}{cal N})-Operators under Functional Calculus 函数微积分下（｛cal A｝｛cl N｝）-算子的稳定性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0231-5
G. Ramesh, H. Osaka, Y. Udagawa, T. Yamazaki
{"title":"Stability of ({cal A}{cal N})-Operators under Functional Calculus","authors":"G. Ramesh,&nbsp;H. Osaka,&nbsp;Y. Udagawa,&nbsp;T. Yamazaki","doi":"10.1007/s10476-023-0231-5","DOIUrl":"10.1007/s10476-023-0231-5","url":null,"abstract":"<div><p>In this note we discuss absolutely norm attaining property (<span>({cal A}{cal N})</span>-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the <span>({cal A}{cal N})</span>-property under the functional calculus. As a consequence we discuss the operator mean of positive <span>({cal A}{cal N})</span>-operators.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0231-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50431404","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
On the Edrei–Goldberg–Ostrovskii Theorem for Minimal Surfaces 关于极小曲面的Edrei-Goldberg-Ostrovskii定理
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0230-6
A. Kowalski, I. I. Marchenko
{"title":"On the Edrei–Goldberg–Ostrovskii Theorem for Minimal Surfaces","authors":"A. Kowalski,&nbsp;I. I. Marchenko","doi":"10.1007/s10476-023-0230-6","DOIUrl":"10.1007/s10476-023-0230-6","url":null,"abstract":"<div><p>This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein’s <i>T</i>*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44302490","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
Building Blocks in Function Spaces 功能空间中的构建块
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-05 DOI: 10.1007/s10476-023-0236-0
H. Triebel
{"title":"Building Blocks in Function Spaces","authors":"H. Triebel","doi":"10.1007/s10476-023-0236-0","DOIUrl":"10.1007/s10476-023-0236-0","url":null,"abstract":"<div><p>The spaces <i>A</i><span>\u0000 <sup><i>s</i></sup><sub><i>p,q</i></sub>\u0000 \u0000 </span>(ℝ<sup><i>n</i></sup>)with <i>A</i> ∈ {<i>B, F</i>}, <i>s</i> ∈ ℝ and 0 &lt;<i>p,q</i> ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces <i>A</i><span>\u0000 <sup><i>s</i></sup><sub><i>p,q</i></sub>\u0000 \u0000 </span>(ℝ<sup><i>n</i></sup>) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions <i>f</i> ∈ <i>S</i>′(ℝ<sup><i>n</i></sup>).</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46285647","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 Φ-Inequalities for Martingale Maximal Operator 鞅极大算子的加权弱型混合Φ-不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-05 DOI: 10.1007/s10476-023-0237-z
Y. Ren
{"title":"Weighted Weak Type Mixed Φ-Inequalities for Martingale Maximal Operator","authors":"Y. Ren","doi":"10.1007/s10476-023-0237-z","DOIUrl":"https://doi.org/10.1007/s10476-023-0237-z","url":null,"abstract":"","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49353985","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 Maximal Operator on Weighted Morrey Spaces 关于加权Morrey空间上最大算子的一个注记
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-05 DOI: 10.1007/s10476-023-0235-1
A. K. Lerner
{"title":"A Note on the Maximal Operator on Weighted Morrey Spaces","authors":"A. K. Lerner","doi":"10.1007/s10476-023-0235-1","DOIUrl":"10.1007/s10476-023-0235-1","url":null,"abstract":"<div><p>In this paper we consider weighted Morrey spaces <span>({cal M}_{lambda ,{cal F}}^p(w))</span> adapted to a family of cubes <span>({cal F})</span>, with the norm </p><div><div><span>$$Vert fVert{_{{cal M}_{lambda ,{cal F}}^p(w)}}: = mathop {sup }limits_{Q in {cal F}} {left( {{1 over {|Q{|^lambda }}}int_Q {|f{|^p}w} } right)^{1/p}},$$</span></div></div><p> and the question we deal with is whether a Muckenhoupt-type condition characterizes the boundedness of the Hardy–Littlewood maximal operator on <span>({cal M}_{lambda ,{cal F}}^p(w))</span>.</p><p>In the case of the global Morrey spaces (when <span>({cal F})</span> is the family of all cubes in ℝ<sup><i>n</i></sup>) this question is still open. In the case of the local Morrey spaces (when <span>({cal F})</span> is the family of all cubes centered at the origin) this question was answered positively in a recent work of Duoandikoetxea and Rosenthal [2].</p><p>We obtain an extension of [2] by showing that the answer is positive when <span>({cal F})</span> is the family of all cubes centered at a sequence of points in ℝ<sup><i>n</i></sup> satisfying a certain lacunary-type condition.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0235-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368608","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
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