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 →
| 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 | |
| Publication status | Published - 2009 Feb 15 |
| Externally published | Yes |
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Keywords
- Generalized Sobolev norms
- Nonlinear inequalities
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras. / Gueorguiev, Vladimir Simeonov; Lucente, Sandra.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 70, No. 4, 15.02.2009, p. 1574-1609.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear and multiplicative inequalities in Sobolev spaces associated with Lie algebras
AU - Gueorguiev, Vladimir Simeonov
AU - Lucente, Sandra
PY - 2009/2/15
Y1 - 2009/2/15
N2 - 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 →
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 →
KW - Generalized Sobolev norms
KW - Nonlinear inequalities
UR - http://www.scopus.com/inward/record.url?scp=57049083025&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=57049083025&partnerID=8YFLogxK
U2 - 10.1016/j.na.2008.02.036
DO - 10.1016/j.na.2008.02.036
M3 - Article
AN - SCOPUS:57049083025
VL - 70
SP - 1574
EP - 1609
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 4
ER -