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arXiv · 0809.4044

On the regularity of maximal operators

Emanuel Carneiro·Diego Moreira
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Abstract

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps $W^{1,p}(\mathbb{R}) \times W^{1,q}(\mathbb{R}) \to W^{1,r}(\mathbb{R})$ with $1 1$. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versions.

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Emanuel Carneiro, Diego Moreira. 2008-09-23. On the regularity of maximal operators. https://doi.org/10.1090/s0002-9939-08-09515-4

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