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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some weighted Gagliardo-Nirenberg inequalities and applications


Authors: Javier Duoandikoetxea and Luis Vega
Journal: Proc. Amer. Math. Soc. 135 (2007), 2795-2802
MSC (2000): Primary 26D10
Published electronically: February 9, 2007
MathSciNet review: 2317954
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Abstract: We obtain conditions on the measure $ \mu$ so that the $ L^2(\mu)$-norm of a function is controlled by the $ L^2$-norms of the function and its gradient. Applications to eigenvalues of the Schrödinger operator and to other inequalites are also given.


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Additional Information

Javier Duoandikoetxea
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao (Spain)
Email: javier.duoandikoetxea@ehu.es

Luis Vega
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao (Spain)
Email: luis.vega@ehu.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08839-9
PII: S 0002-9939(07)08839-9
Received by editor(s): February 22, 2006
Received by editor(s) in revised form: May 12, 2006
Published electronically: February 9, 2007
Additional Notes: The first author was supported by the grant MTM2005-08430 of MEC (Spain) and FEDER. The second author was supported by the grant MTM 2004-03029 of MEC (Spain) and FEDER. Both authors were supported by the European Project HPRN-CT-2001-00273-HARP
Communicated by: Andreas Seeger
Article copyright: © Copyright 2007 American Mathematical Society