Complete Sobolev Type Inequalities

2020/08/21 by Li, Haojian
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2008.09278

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.

Related

• Interpolation between modified logarithmic Sobolev and Poincare inequalities for quantum Markovian dynamics
• Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces
• Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
• Curvature-dimension conditions for symmetric quantum Markov semigroups
• Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions