On a discrete version of Tanaka's theorem for maximal functions

Jonathan W Bober, Emanuel Carnerio, Kevin Hughes, Lillian Pierce

Research output: Contribution to journalArticle (Academic Journal)peer-review

32 Citations (Scopus)

Abstract

In this paper we prove a discrete version of Tanaka's theorem for the Hardy-Littlewood maximal operator in dimension , both in the non-centered and centered cases. For the non-centered maximal operator we prove that, given a function of bounded variation,




where represents the total variation of . For the centered maximal operator we prove that, given a function such that ,



This provides a positive solution to a question of Hajłasz and Onninen in the discrete one-dimensional case.
Original languageEnglish
Pages (from-to)1669-1680
Number of pages12
JournalProceedings of the American Mathematical Society
Volume140
Issue number5
DOIs
Publication statusPublished - 2012

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