Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras

Vladimir Georgiev; Sandra Lucente

doi:10.1016/j.na.2008.02.036

Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras

Vladimir Georgiev, Sandra Lucente^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 non-regular 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 → | u |^p acts on such spaces.

Original language	English
Pages (from-to)	1574-1609
Number of pages	36
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	70
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2008.02.036
Publication status	Published - 2009 Feb 15
Externally published	Yes

Keywords

Generalized Sobolev norms
Nonlinear inequalities

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2008.02.036

Cite this

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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 non-regular 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 → | u |p acts on such spaces.",

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AU - Lucente, Sandra

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AB - 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 non-regular 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 → | u |p acts on such spaces.

KW - Generalized Sobolev norms

KW - Nonlinear inequalities

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ER -

Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras

Abstract

Keywords

ASJC Scopus subject areas

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