Interpolation between logarithmic Sobolev and Poincare inequalities
Arnold, Anton ; Bartier, Jean-Philippe ; Dolbeault, Jean
Commun. Math. Sci., Tome 5 (2007) no. 1, p. 971-979 / Harvested from Project Euclid
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This paper is concerned with intermediate inequalities which interpolate between the logarithmic Sobolev (LSI) and the Poincaré inequalities. Assuming that a given probability measure gives rise to a LSI, we derive generalized Poincaré inequalities, improving upon the known constants from the literature. We also analyze the special case when these inequalities are restricted to functions with zero components for the first eigenspaces of the corresponding evolution operator.
Publié le : 2007-12-15
Classification:  functional inequalities,  Poincaré inequality,  logarithmic Sobolev inequality,  spectral gap,  hypercontractivity,  39B62,  46E35,  35K10,  60J60,  60F10 
@article{1199377560,
     author = {Arnold, Anton and Bartier, Jean-Philippe and Dolbeault, Jean},
     title = {Interpolation between logarithmic Sobolev and Poincare inequalities},
     journal = {Commun. Math. Sci.},
     volume = {5},
     number = {1},
     year = {2007},
     pages = { 971-979},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1199377560}
}

Arnold, Anton; Bartier, Jean-Philippe; Dolbeault, Jean. Interpolation between logarithmic Sobolev and Poincare inequalities. Commun. Math. Sci., Tome 5 (2007) no. 1, pp.  971-979. http://gdmltest.u-ga.fr/item/1199377560/