This paper is devoted to multiplicative inequalities in some generalized Sobolev spaces associated with Lie algebras. These Lie algebras are generated by the differential operator of variable coefficients or by pseudo-differential operators having nonregular symbols. Under geometrical assumptions we show that the norms of two suitable classes of generalized Sobolev spaces are equivalent. This leads to the proof that the composition operator u -> vertical bar u vertical bar(p) acts on such spaces. (C) 2008 Elsevier Ltd. All rights reserved.
Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras
LUCENTE, SANDRA
2009-01-01
Abstract
This paper is devoted to multiplicative inequalities in some generalized Sobolev spaces associated with Lie algebras. These Lie algebras are generated by the differential operator of variable coefficients or by pseudo-differential operators having nonregular symbols. Under geometrical assumptions we show that the norms of two suitable classes of generalized Sobolev spaces are equivalent. This leads to the proof that the composition operator u -> vertical bar u vertical bar(p) acts on such spaces. (C) 2008 Elsevier Ltd. All rights reserved.File in questo prodotto:
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