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A class of bounded operators on Sobolev spaces

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693456
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Submitted on : Wednesday, May 2, 2012 - 4:54:36 PM
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S Korry. A class of bounded operators on Sobolev spaces. Archiv der Mathematik, Springer Verlag, 2004, 82 (1), pp.40--50. ⟨10.1007/s00013-003-0416-x⟩. ⟨hal-00693456⟩

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