On the Regularity of Maximal Operators
نویسنده
چکیده
We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W (R) × W (R) → W (R) with 1 < p, q < ∞ and r ≥ 1, boundedly and continuously. The same result holds on R when r > 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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