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On the variation of maximal operators of convolution type (1309.1529v1)
Published 6 Sep 2013 in math.AP, math.CA, and math.FA
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 $Lp$-variation of a function for any $p \geq 1$, while in dimensions $d>1$ we obtain the corresponding results for the $L2$-variation. Similar results are proved for the discrete versions of these operators.