On the regularity of maximal operators

By Emanuel Carneiro, Diego R. Moreira. 2008

64 citations recorded by the source corpus.

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W 1,p (R) × W 1,q (R) → W 1,r (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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dbaaf52915266cdf92b39c1a324658fe42861100

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Corrigendum to “On a discrete version of Tanaka’s theorem for maximal functions” (2010, background): “ the program started in 1998 by Kinunnen [9] that studies the regularity of maximal operators acting on Sobolev functions. Since then, many authors have contributed to extend the theory, for instance [4], [5], [10], [11], [12], always having in the background the general principle that, for maximal ”
On the variation of maximal operators of convolution type (2013, background): “The paradigm that an L-bound implies a W -bound was later extended to a local version of M in [10], to a fractional version in [11] and to a multilinear version in [5].”
Derivative bounds for fractional maximal functions (2015, unknown): “This paradigm has been extended to multilinear, local and fractional contexts in [7,12,13].”
On the endpoint regularity of discrete maximal operators (2013, unknown): “This paradigm that an L-bound implies a W -bound was later extended to a local version of the maximal operator [9], to a fractional version [10] and to a multilinear version [5].”
On approximate differentiability of the maximal function (2010, background): “Let us also mention that the result of Kinnunen [10] has been applied and generalized by many authors ([2], [3], [6], [7], [8], [11], [12], [14], [15], [16], [17], [18], [20], [21], [25]).”