On the variation of maximal operators of convolution type

By Emanuel Carneiro, Benar Fux Svaiter. 2013

72 citations recorded by the source corpus.

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 ⩾ 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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/24841490b849e6b47dba4865712d10e7e40abefa

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In Applied Mathematics

1. Jos'e Madrid
2. Emanuel Carneiro
3. Shuanglin Shao
4. Aynur Bulut
5. William Beckner

Citations in the corpus

• Derivative bounds for fractional maximal functions (2015, background): “In [8], Carneiro and Svaiter considered maximal operators of convolution type associated to smooth kernels (namely, the Gauss kernel and the Poisson kernel) and obtained the inequalities (1.”
• On the endpoint regularity of discrete maximal operators (2013, unknown): “Regularity results of similar flavour for the heat flow maximal operator and the Poisson maximal operator were obtained in [6].”