Some weighted Gagliardo-Nirenberg inequalities and applications
HTML articles powered by AMS MathViewer
- by Javier Duoandikoetxea and Luis Vega PDF
- Proc. Amer. Math. Soc. 135 (2007), 2795-2802 Request permission
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.References
- William Beckner, Pitt’s inequality and the uncertainty principle, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1897–1905. MR 1254832, DOI 10.1090/S0002-9939-1995-1254832-9
- Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
- L. Caffarelli, R. Kohn, and L. Nirenberg, First order interpolation inequalities with weights, Compositio Math. 53 (1984), no. 3, 259–275. MR 768824
- Jean Dolbeault, Maria J. Esteban, and Eric Séré, On the eigenvalues of operators with gaps. Application to Dirac operators, J. Funct. Anal. 174 (2000), no. 1, 208–226. MR 1761368, DOI 10.1006/jfan.1999.3542
- Elliott H. Lieb and Michael Loss, Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 1997. MR 1415616, DOI 10.2307/3621022
- Chang Shou Lin, Interpolation inequalities with weights, Comm. Partial Differential Equations 11 (1986), no. 14, 1515–1538. MR 864416, DOI 10.1080/03605308608820473
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)
- MR Author ID: 237776
- Email: luis.vega@ehu.es
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2795-2802
- MSC (2000): Primary 26D10
- DOI: https://doi.org/10.1090/S0002-9939-07-08839-9
- MathSciNet review: 2317954