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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":"50 1","pages":"295 - 322"},"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":"49 4","pages":"895 - 950"},"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":"49 4","pages":"971 - 1006"},"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":"49 4","pages":"891 - 893"},"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
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":"49 4","pages":"1137 - 1174"},"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":"49 4","pages":"1087 - 1106"},"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":"49 4","pages":"1007 - 1039"},"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":"49 4","pages":"951 - 969"},"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":"49 4","pages":"1041 - 1052"},"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":"49 4","pages":"1053 - 1071"},"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
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