{"title":"A Derivative-Free Characterization of the Weighted Besov Spaces","authors":"W. Pan, H. Wulan","doi":"10.1007/s10476-023-0187-5","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain a characterization of the weighted Besov space <span>\\({{\\cal B}_K}\\left( p \\right)\\)</span> for a weight function <i>K</i>, 0 < <i>p</i> < ∞, in terms of symmetric and derivative-free double integrals with the weight function <i>K</i> in the unit disc. As a by-product, we give a modification of the identity of Littlewood—Paley type for the Bergman space. As an application, a derivative-free characterization of <span>\\({{\\cal Q}_K}\\)</span> type spaces is obtained.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0187-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain a characterization of the weighted Besov space \({{\cal B}_K}\left( p \right)\) for a weight function K, 0 < p < ∞, in terms of symmetric and derivative-free double integrals with the weight function K in the unit disc. As a by-product, we give a modification of the identity of Littlewood—Paley type for the Bergman space. As an application, a derivative-free characterization of \({{\cal Q}_K}\) type spaces is obtained.
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.