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arXiv · 1309.1529

On the variation of maximal operators of convolution type

Emanuel Carneiro·Benar F. Svaiter
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Abstract

In this paper we study the regularity properties of two maximal operators of convolution type: the heat flow maximal operator (associated to the Gauss kernel) and the Poisson maximal operator (associated to the Poisson kernel). In dimension $d=1$ we prove that these maximal operators do not increase the $L^p$-variation of a function for any $p \geq 1$, while in dimensions $d>1$ we obtain the corresponding results for the $L^2$-variation. Similar results are proved for the discrete versions of these operators.

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Emanuel Carneiro, Benar F. Svaiter. 2013-09-06. On the variation of maximal operators of convolution type. https://doi.org/10.1016/j.jfa.2013.05.012

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