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 on such spaces.
Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras
GUEORGUIEV, VLADIMIR SIMEONOV;
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 on such spaces.File in questo prodotto:
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