Complete Sobolev Type Inequalities
Differential Geometry
2020-08-24 v1 Mathematical Physics
Functional Analysis
math.MP
Probability
Abstract
We establish Sobolev type inequalities in the noncommutative settings by generalizing monotone metrics in the space of quantum states, such as matrix-valued Beckner inequalities. We also discuss examples such as random transpositions and Bernoulli-Laplace models.
Cite
@article{arxiv.2008.09278,
title = {Complete Sobolev Type Inequalities},
author = {Haojian Li},
journal= {arXiv preprint arXiv:2008.09278},
year = {2020}
}