Archiv der Mathematik

, Volume 82, Issue 1, pp 40–50

A class of bounded operators on Sobolev spaces

Original paper
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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.

Mathematics Subject Classification (2000):

46E40 46E35. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Equipe d’Analyse et de Mathématiques AppliquéesUniversité de Marne-La-ValléeMarne-La-Vallée Cedex 2France

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