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SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION

Published online by Cambridge University Press:  04 November 2016

JOSÉ MADRID*
Affiliation:
IMPA—Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil email [email protected]
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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].

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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