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Derivative bounds for fractional maximal functions


Authors: Emanuel Carneiro and José Madrid
Journal: Trans. Amer. Math. Soc. 369 (2017), 4063-4092
MSC (2010): Primary 26A45, 42B25, 39A12, 46E35, 46E39
DOI: https://doi.org/10.1090/tran/6844
Published electronically: June 10, 2016
MathSciNet review: 3624402
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Abstract: In this paper we study the regularity properties of fractional maximal operators acting on $ BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.


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Additional Information

Emanuel Carneiro
Affiliation: IMPA - Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro - RJ, Brazil, 22460-320
Email: carneiro@impa.br

José Madrid
Affiliation: IMPA - Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro - RJ, Brazil, 22460-320
Email: josermp@impa.br

DOI: https://doi.org/10.1090/tran/6844
Keywords: Fractional maximal operator, Sobolev spaces, discrete maximal operators, bounded variation
Received by editor(s): June 4, 2015
Published electronically: June 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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