{"title":"A sharp two-weight estimate for the maximal operator under a bump condition","authors":"Adam Osękowski","doi":"10.1007/s00605-023-01932-0","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\({\\mathcal {M}}_{\\mathcal {D}}\\)</span> be the dyadic maximal operator on <span>\\({\\mathbb {R}}^n\\)</span>. The paper contains the identification of the best constant in the two-weight estimate </p><span>$$\\begin{aligned} \\Vert {\\mathcal {M}}_{\\mathcal {D}}f\\Vert _{L^p(w)}\\le C_{p,\\sigma ,w}\\Vert f\\Vert _{L^p(\\sigma ^{1-p})} \\end{aligned}$$</span><p>under the assumption that the pair <span>\\((\\sigma ,w)\\)</span> of weights satisfies an appropriate bump condition. The result is shown to be true in the larger context of abstract probability spaces equipped with a tree-like structure.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-023-01932-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let \({\mathcal {M}}_{\mathcal {D}}\) be the dyadic maximal operator on \({\mathbb {R}}^n\). The paper contains the identification of the best constant in the two-weight estimate
under the assumption that the pair \((\sigma ,w)\) of weights satisfies an appropriate bump condition. The result is shown to be true in the larger context of abstract probability spaces equipped with a tree-like structure.