{"title":"A molecular reconstruction theorem for $$H^{p(\\cdot )}_{\\omega }(\\mathbb {R}^{n})$$","authors":"Pablo Rocha","doi":"10.1007/s10998-024-00575-4","DOIUrl":null,"url":null,"abstract":"<p>In this article we give a molecular reconstruction theorem for <span>\\(H_{\\omega }^{p(\\cdot )}(\\mathbb {R}^{n})\\)</span>. As an application of this result and the atomic decomposition developed in Ho (Tohoku Math J 69 (3), 383–413, 2017) we show that classical singular integrals can be extended to bounded operators on <span>\\(H_{\\omega }^{p(\\cdot )}(\\mathbb {R}^{n})\\)</span>. We also prove, for certain exponents <span>\\(q(\\cdot )\\)</span> and certain weights <span>\\(\\omega \\)</span>, that the Riesz potential <span>\\(I_{\\alpha }\\)</span>, with <span>\\(0< \\alpha < n\\)</span>, can be extended to a bounded operator from <span>\\(H^{p(\\cdot )}_{\\omega }(\\mathbb {R}^{n})\\)</span> into <span>\\(H^{q(\\cdot )}_{\\omega }(\\mathbb {R}^{n})\\)</span>, for <span>\\(\\frac{1}{p(\\cdot )}:= \\frac{1}{q(\\cdot )} + \\frac{\\alpha }{n}\\)</span>.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"18 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Periodica Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00575-4","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
In this article we give a molecular reconstruction theorem for \(H_{\omega }^{p(\cdot )}(\mathbb {R}^{n})\). As an application of this result and the atomic decomposition developed in Ho (Tohoku Math J 69 (3), 383–413, 2017) we show that classical singular integrals can be extended to bounded operators on \(H_{\omega }^{p(\cdot )}(\mathbb {R}^{n})\). We also prove, for certain exponents \(q(\cdot )\) and certain weights \(\omega \), that the Riesz potential \(I_{\alpha }\), with \(0< \alpha < n\), can be extended to a bounded operator from \(H^{p(\cdot )}_{\omega }(\mathbb {R}^{n})\) into \(H^{q(\cdot )}_{\omega }(\mathbb {R}^{n})\), for \(\frac{1}{p(\cdot )}:= \frac{1}{q(\cdot )} + \frac{\alpha }{n}\).
期刊介绍:
Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica.
Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.