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A class of bounded operators on Sobolev spaces

Authors:	Email author" target="_blank">S?Korry Email author

Institution:	(1) Equipe dAnalyse et de Mathématiques Appliquées, Université de Marne-La-Vallée, 5, Bd. Descartes Champs-sur-Marne, 77454 Marne-La-Vallée Cedex 2, France

Abstract:	We describe a class of nonlinear operators which are bounded on the Sobolev spaces $H^{s}_{p}(\mathbb{R}^n)$ , for $0 \leq s \leq 1$ and 1 < p < $\infty$ . As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on $H^{s}_{p}(\mathbb{R}^n)$ , for $0 \leq s \leq 1$ and 1 < p < $\infty$ ; this extends the result of J. Kinnunen 7], valid for s = 1. Received: 5 December 2000

Keywords:	46E40 46E35
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