scholarly journals Logarithmic Derivatives of Heat Kernels and Logarithmic Sobolev Inequalities with Unbounded Diffusion Coefficients on Loop Spaces

2000 ◽  
Vol 174 (2) ◽  
pp. 430-477 ◽  
Author(s):  
Shigeki Aida
Keyword(s):  
Diffusion Coefficients ◽  
Heat Kernels ◽  
Sobolev Inequalities ◽  
Loop Spaces ◽  
Logarithmic Sobolev Inequalities ◽  
Derivatives Of ◽  
Logarithmic Derivatives

BEYOND STRONG SUBADDITIVITY? IMPROVED BOUNDS ON THE CONTRACTION OF GENERALIZED RELATIVE ENTROPY

1994 ◽  
Vol 06 (05a) ◽  
pp. 1147-1161 ◽  
Author(s):  
MARY BETH RUSKAI
Keyword(s):  
Relative Entropy ◽  
Discrete Case ◽  
Sobolev Inequalities ◽  
Completely Positive ◽  
Logarithmic Sobolev Inequalities ◽  
Strong Subadditivity

New bounds are given on the contraction of certain generalized forms of the relative entropy of two positive semi-definite operators under completely positive mappings. In addition, several conjectures are presented, one of which would give a strengthening of strong subadditivity. As an application of these bounds in the classical discrete case, a new proof of 2-point logarithmic Sobolev inequalities is presented in an Appendix.

scholarly journals Complete logarithmic Sobolev inequalities via Ricci curvature bounded below

2022 ◽  
Vol 394 ◽  
pp. 108129
Author(s):  
Michael Brannan ◽  
Li Gao ◽  
Marius Junge
Keyword(s):  
Ricci Curvature ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities ◽  
Bounded Below

On Logarithmic Derivatives of Functions in a Class of Starlike Mappings

1993 ◽  
Vol 36 (1) ◽  
pp. 38-44
Author(s):  
Alan D. Gluchoff
Keyword(s):  
Integral Means ◽  
Koebe Function ◽  
Starlike Mappings ◽  
Derivatives Of ◽  
Logarithmic Derivatives

AbstractThe purpose of this paper is to prove some facts about integral means of (d2/dz2)(log[f(z)/z])—or equivalently f″/f, for f in a class of starlike mappings of a "singular" nature. In particular it is noted that the Koebe function is not extremal for the Hardy means Mp(r,f″/f) for functions in this class.

Reduced Sobolev Inequalities

1988 ◽  
Vol 31 (2) ◽  
pp. 159-167 ◽  
Author(s):  
R. A. Adams
Keyword(s):  
Compact Support ◽  
Sobolev Inequality ◽  
Smooth Function ◽  
Sobolev Inequalities ◽  
Partial Derivatives ◽  
Derivatives Of

AbstractThe Sobolev inequality of order m asserts that if p ≧ 1, mp < n and 1/q = 1/p — m/n, then the Lq-norm of a smooth function with compact support in Rn is bounded by a constant times the sum of the Lp-norms of the partial derivatives of order m of that function. In this paper we show that that sum may be reduced to include only the completely mixed partial derivatives or order m, and in some circumstances even fewer partial derivatives.

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