{"title":"Application of Perron trees to\ngeometric maximal operators","authors":"A. Gauvan","doi":"10.4064/cm8693-8-2022","DOIUrl":null,"url":null,"abstract":"We characterize the L p ( R 2 ) boundeness of the geometric maximal operator M a,b associated to the basis B a,b ( a, b > 0) which is composed of rectangles R whose eccentricity and orientation is of the form ( e R , ω R ) = (cid:18) 1 n a , π 4 n b (cid:19) for some n ∈ N ∗ . The proof involves generalized Perron trees , as constructed in [12].","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/cm8693-8-2022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
We characterize the L p ( R 2 ) boundeness of the geometric maximal operator M a,b associated to the basis B a,b ( a, b > 0) which is composed of rectangles R whose eccentricity and orientation is of the form ( e R , ω R ) = (cid:18) 1 n a , π 4 n b (cid:19) for some n ∈ N ∗ . The proof involves generalized Perron trees , as constructed in [12].
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