scholarly journals On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group

2020 ◽  
Vol 29 (2) ◽  
pp. 335-355 ◽  
Author(s):  
Michel Bonnefont ◽  
Djalil Chafaï ◽  
Ronan Herry
Keyword(s):  
Heisenberg Group ◽  
Heat Kernel ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities

scholarly journals Coercive inequalities in higher-dimensional anisotropic heisenberg group

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Esther Bou Dagher ◽  
Bogusław Zegarliński
Keyword(s):  
Fundamental Solution ◽  
Heisenberg Group ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities ◽  
Higher Dimensional

AbstractIn the setting of higher-dimensional anisotropic Heisenberg group, we compute the fundamental solution for the sub-Laplacian, and we prove Poincaré and $$\beta $$ β -Logarithmic Sobolev inequalities for measures as a function of this fundamental solution.

scholarly journals Optimal heat kernel bounds under logarithmic Sobolev inequalities

1997 ◽  
Vol 1 ◽  
pp. 391-407 ◽  
Author(s):  
Dominique Bakry ◽  
Daniel Concordet ◽  
Michel Ledoux
Keyword(s):  
Heat Kernel ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities ◽  
Optimal Heat ◽  
Kernel Bounds

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.

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