{"title":"On Entropy Bumps for Calderón-Zygmund Operators","authors":"M. Lacey, Scott Spencer","doi":"10.1515/conop-2015-0003","DOIUrl":null,"url":null,"abstract":"Abstract We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"2 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2015-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2015-0003","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2015-0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 16
Abstract
Abstract We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).
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