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Sobolev Inequality and the Exact Multiplicity of

โœ Scribed by Yuqiang Feng

Publisher
Springer Netherlands
Year
2009
Tongue
English
Weight
299 KB
Volume
110
Category
Article
ISSN
0167-8019

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We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587 600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities. Conversely, Talagrand's inequality implies a logarithmic Sobolev inequality if the density of the measure i