{"title":"各向异性Besov空间的重排估计和限制嵌入","authors":"V. I. Kolyada","doi":"10.1007/s10476-023-0241-3","DOIUrl":null,"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> < 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":0.6000,"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":"0","resultStr":"{\"title\":\"Rearrangement Estimates and Limiting Embeddings for Anisotropic Besov Spaces\",\"authors\":\"V. I. Kolyada\",\"doi\":\"10.1007/s10476-023-0241-3\",\"DOIUrl\":null,\"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> < 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\":0.6000,\"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\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-023-0241-3\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0241-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Rearrangement Estimates and Limiting Embeddings for Anisotropic Besov Spaces
The paper is dedicated to the study of embeddings of the anisotropic Besov spaces \(B_{p,{\theta _1}, \ldots ,{\theta _n}}^{{\beta _1}, \ldots ,{\beta _n}}\) (ℝn) into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of the exponents βk tend to 1 (βk < 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.
One of the key results of the paper is an anisotropic type estimate of rearrangements in terms of partial moduli of continuity.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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