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SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION

Part of: Real functions Difference equations Harmonic analysis in several variables Difference and functional equations Linear function spaces and their duals

Published online by Cambridge University Press:  04 November 2016

JOSÉ MADRID
JOSÉ MADRID*
Affiliation:
IMPA—Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil email josermp@impa.br
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Abstract

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In this paper we establish new optimal bounds for the derivative of some discrete maximal functions, in both the centred and uncentred versions. In particular, we solve a question originally posed by Bober et al. [‘On a discrete version of Tanaka’s theorem for maximal functions’, Proc. Amer. Math. Soc.140 (2012), 1669–1680].

Keywords

Sobolev spacesdiscrete maximal operatorsbounded variation

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 26A45: Functions of bounded variation, generalizations 39A12: Discrete version of topics in analysis 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E39: Sobolev (and similar kinds of) spaces of functions of discrete variables
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 1 , February 2017 , pp. 94 - 107
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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