%0 Journal Article
%T On the variation of maximal operators of convolution type
%A Emanuel Carneiro
%A Benar F. Svaiter
%J Mathematics
%D 2013
%I arXiv
%R 10.1016/j.jfa.2013.05.012
%X 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.
%U http://arxiv.org/abs/1309.1529v1