A class of bounded operators on Sobolev spaces

S Korry (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We describe a class of nonlinear operators which are bounded on the Sobolev spaces H-P(S)(R-n), for 0 less than or equal to s less than or equal to 1 and 1 < p < infinity. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on H-P(S) (R-n), for 0 less than or equal to s less than or equal to 1 and 1 < p < infinity; this extends the result of J. Kinnunen [7], valid for s = 1.

Domaines: Physique mathématique [math-ph]

S Korry. A class of bounded operators on Sobolev spaces. Archiv der Mathematik, 2004, 82 (1), pp.40--50. ⟨10.1007/s00013-003-0416-x⟩. ⟨hal-00693456⟩