Archiv der Mathematik

, Volume 82, Issue 1, pp 40–50

A class of bounded operators on Sobolev spaces

Original paper

DOI: 10.1007/s00013-003-0416-x

Cite this article as:
Korry, S. Arch. Math. (2004) 82: 40. doi:10.1007/s00013-003-0416-x

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):

46E4046E35.

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