Complete Sobolev Type Inequalities

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.

References in corpus (2)

• On the joint convexity of the Bregman divergence of matrices
• Graph Hörmander Systems