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Boundedness of the Hilbert Transform in Besov Spaces Besov空间中Hilbert变换的有界性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-11-15 DOI: 10.1007/s10476-023-0242-2
E. P. Ushakova
{"title":"Boundedness of the Hilbert Transform in Besov Spaces","authors":"E. P. Ushakova","doi":"10.1007/s10476-023-0242-2","DOIUrl":"10.1007/s10476-023-0242-2","url":null,"abstract":"<div><p>Boundedness conditions are found for the Hilbert transform <i>H</i> in Besov spaces with Muckenhoupt weights. The operator <i>H</i> in this situation acts on subclasses of functions from Hardy spaces. The results are obtained by representing the Hilbert transform <i>H</i> via Riemann–Liouville operators of fractional integration on ℝ, on the norms of images and pre-images of which independent estimates are established in the paper. Separately, a boundedness criterion is given for the transform <i>H</i> in weighted Besov and Triebel–Lizorkin spaces restricted to the subclass of Schwartz functions.</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/s10476-023-0242-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796399","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
Grand Lebesgue Spaces with Mixed Local and Global Aggrandization and the Maximal and Singular Operators 局部和全局混合扩张的大Lebesgue空间及其极大算子和奇异算子
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-10-28 DOI: 10.1007/s10476-023-0243-1
H. Rafeiro, S. Samko, S. Umarkhadzhiev
{"title":"Grand Lebesgue Spaces with Mixed Local and Global Aggrandization and the Maximal and Singular Operators","authors":"H. Rafeiro,&nbsp;S. Samko,&nbsp;S. Umarkhadzhiev","doi":"10.1007/s10476-023-0243-1","DOIUrl":"10.1007/s10476-023-0243-1","url":null,"abstract":"<div><p>The approach to “locally” aggrandize Lebesgue spaces, previously suggested by the authors and based on the notion of “aggrandizer”, is combined with the usual “global” aggrandization. We study properties of such spaces including embeddings, dependence of the choice of the aggrandizer and, in particular, we discuss the question when these spaces are not new, coinciding with globally aggrandized spaces, and when they proved to be new. We study the boundedness of the maximal, singular, and maximal singular operators in the introduced spaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0243-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797686","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
Nuclear and Compact Embeddings in Function Spaces of Generalised Smoothness 广义光滑函数空间中的核嵌入与紧嵌入
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-10-09 DOI: 10.1007/s10476-023-0238-y
D. D. Haroske, H.-G. Leopold, S. D. Moura, L. Skrzypczak
{"title":"Nuclear and Compact Embeddings in Function Spaces of Generalised Smoothness","authors":"D. D. Haroske,&nbsp;H.-G. Leopold,&nbsp;S. D. Moura,&nbsp;L. Skrzypczak","doi":"10.1007/s10476-023-0238-y","DOIUrl":"10.1007/s10476-023-0238-y","url":null,"abstract":"<div><p>We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain Ω ⊂ ℝ<sup><i>d</i></sup>. This covers, in particular, the well-known situation for spaces of Besov and Triebel–Lizorkin spaces defined on bounded domains as well as some first results for function spaces of logarithmic smoothness. In addition, we provide some new, more general approach to compact embeddings for such function spaces, which also unifies earlier results in different settings, including also the study of their entropy numbers. Again we rely on suitable wavelet decomposition techniques and the famous Tong result (1969) about nuclear diagonal operators acting in <i>∓</i><sub><i>r</i></sub> spaces, which we could recently extend to the vector-valued setting needed here.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0238-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795697","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
Diversity of Lorentz-Zygmund Spaces of Operators Defined by Approximation Numbers 由近似数定义的算子的Lorentz-Zygmund空间的多样性
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-10-09 DOI: 10.1007/s10476-023-0239-x
F. Cobos, T. Kühn
{"title":"Diversity of Lorentz-Zygmund Spaces of Operators Defined by Approximation Numbers","authors":"F. Cobos,&nbsp;T. Kühn","doi":"10.1007/s10476-023-0239-x","DOIUrl":"10.1007/s10476-023-0239-x","url":null,"abstract":"<div><p>We prove the following dichotomy for the spaces <i>ℒ</i><span>\u0000 <sup>(<i>a</i>)</sup><sub><i>p</i>,<i>q</i>,<i>α</i></sub>\u0000 \u0000 </span> (<i>X</i>, <i>Y</i>) of all operators <i>T</i> ∈ <i>ℒ</i>(<i>X</i>, <i>Y</i>) whose approximation numbers belong to the Lorentz-Zygmund sequence spaces <i>ℓ</i><sub><i>p</i>,<i>q</i></sub>(log <i>ℓ</i>)<sub><i>α</i></sub>: If <i>X</i> and <i>Y</i> are <i>infinite-dimensional</i> Banach spaces, then the spaces <i>ℒ</i><span>\u0000 <sup>(<i>a</i>)</sup><sub><i>p</i>,<i>q</i>,<i>α</i></sub>\u0000 \u0000 </span>(<i>X</i>, <i>Y</i>) with 0 &lt; <i>p</i> &lt; ∞, 0 &lt; <i>q</i> ≤ ∞ and <i>α</i> ∈ ℝ are all different from each other, but otherwise, if <i>X</i> or <i>Y</i> are <i>finite-dimensional</i>, they are all equal (to <i>ℒ</i>(<i>X</i>, <i>Y</i>)).</p><p>Moreover we show that the scale <span>({{ {cal L}_{infty ,q}^{(a)}(X,Y)} _{0, &lt; q, &lt; infty }})</span> is strictly increasing in <i>q</i>, where <i>ℒ</i><span>\u0000 <sup>(<i>a</i>)</sup><sub>∈,<i>q</i></sub>\u0000 \u0000 </span>(<i>X</i>, <i>Y</i>) is the space of all operators in <i>ℒ</i>(<i>X</i>, <i>Y</i>) whose approximation numbers are in the limiting Lorentz sequence space <i>∓</i><sub>∈,<i>q</i></sub>.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0239-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795731","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: 1
Two Weighted Norm Inequalities of Potential Type Operator on Herz Spaces 赫兹空间上势型算子的两个加权范数不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-10-09 DOI: 10.1007/s10476-023-0240-4
K.-P. Ho, T.-L. Yee
{"title":"Two Weighted Norm Inequalities of Potential Type Operator on Herz Spaces","authors":"K.-P. Ho,&nbsp;T.-L. Yee","doi":"10.1007/s10476-023-0240-4","DOIUrl":"10.1007/s10476-023-0240-4","url":null,"abstract":"<div><p>We extend the two weighted norm inequalities for the potential type operators to Herz spaces. As an application of this result, we have the two weighted norm inequalities of the fractional integral operators on Herz spaces.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0240-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795698","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
Rearrangement Estimates and Limiting Embeddings for Anisotropic Besov Spaces 各向异性Besov空间的重排估计和限制嵌入
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-10-09 DOI: 10.1007/s10476-023-0241-3
V. I. Kolyada
{"title":"Rearrangement Estimates and Limiting Embeddings for Anisotropic Besov Spaces","authors":"V. I. Kolyada","doi":"10.1007/s10476-023-0241-3","DOIUrl":"10.1007/s10476-023-0241-3","url":null,"abstract":"<div><p>The paper is dedicated to the study of embeddings of the anisotropic Besov spaces <span>(B_{p,{theta _1}, ldots ,{theta _n}}^{{beta _1}, ldots ,{beta _n}})</span> (ℝ<sup><i>n</i></sup>) into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of the exponents <i>β</i><sub><i>k</i></sub> tend to 1 (<i>β</i><sub><i>k</i></sub> &lt; 1). In particular, these results give an extension of the estimate proved by Bourgain, Brezis, and Mironescu for isotropic Besov spaces. Also, in the limit, we obtain a link with some known embeddings of anisotropic Lipschitz spaces.</p><p>One of the key results of the paper is an anisotropic type estimate of rearrangements in terms of partial moduli of continuity.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10476-023-0241-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134878266","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
Kolmogorov and Markov Type Inequalities on Certain Algebraic Varieties 若干代数变种上的Kolmogorov和Markov型不等式
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0224-4
T. Beberok
{"title":"Kolmogorov and Markov Type Inequalities on Certain Algebraic Varieties","authors":"T. Beberok","doi":"10.1007/s10476-023-0224-4","DOIUrl":"10.1007/s10476-023-0224-4","url":null,"abstract":"<div><p>In this paper we introduce a generalization to compact subsets of certain algebraic varieties of the classical Markov inequality on the derivatives of a polynomial in terms of its own values. We also introduce an extension to such sets of a local form of the classical Markov inequality, and show the equivalence of introduced Markov and local Markov inequalities.</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":"45005511","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
Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density 具有有界密度谱的欧氏空间上的傅立叶拟晶及其分布
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0228-0
S. Yu. Favorov
{"title":"Fourier Quasicrystals and Distributions on Euclidean Spaces with Spectrum of Bounded Density","authors":"S. Yu. Favorov","doi":"10.1007/s10476-023-0228-0","DOIUrl":"10.1007/s10476-023-0228-0","url":null,"abstract":"<div><p>We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sums of derivatives of generalized lattice Dirac combs. These theorems are derived from properties of families of discretely supported measures and almost periodic distributions.</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/s10476-023-0228-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49043400","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: 1
Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges 关于二重规的Hewitt-Stromberg测度的一些正则性质
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0227-1
Z. Douzi, B. Selmi, Z. Yuan
{"title":"Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges","authors":"Z. Douzi,&nbsp;B. Selmi,&nbsp;Z. Yuan","doi":"10.1007/s10476-023-0227-1","DOIUrl":"10.1007/s10476-023-0227-1","url":null,"abstract":"<div><p>The aim of this paper is to show that if the Hewitt–Stromberg pre-measures with respect to the gauge are finite, then these pre-measures have a kind of <i>outer regularity</i> in a general metric space <i>X</i>. We give also some conditions on the Hewitt–Stromberg pre-measures with respect to the gauge such that the Hewitt–Stromberg measures have an almost <i>inner regularity</i> on a complete separable metric space <i>X</i>.</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":"45161713","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 Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps 向量值可微映射空间的Banach-Stone型定理
IF 0.7 3区 数学
Analysis Mathematica Pub Date : 2023-09-06 DOI: 10.1007/s10476-023-0232-4
A. Ranjbar-Motlagh
{"title":"A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps","authors":"A. Ranjbar-Motlagh","doi":"10.1007/s10476-023-0232-4","DOIUrl":"10.1007/s10476-023-0232-4","url":null,"abstract":"<div><p>This article describes the surjective linear isometries between spaces of <i>p</i>-times differentiable maps from a domain of the Euclidean space into a certain Banach space.</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":"44727164","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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