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Special Session 88: Recent developments in stochastic analysis and related topics

Symmetry and functional inequalities for stable Levy-type operators
Lu-Jing Huang
Fujian Normal University
Peoples Rep of China
Co-Author(s):    Tao Wang
Abstract:
In this talk, we establish the sufficient and necessary conditions for the symmetry of the following stable L\`evy-type operator L on R: L=a(x)Δα/2+b(x)ddx, where a,b are the continuous positive and differentiable functions, respectively. We then study the criteria for functional inequalities, such as logarithmic Sobolev inequalities, Nash inequalities and super-Poincar\`e inequalities under the assumption of symmetry. Our approach involves the Orlicz space theory and the estimates of the Green functions. This is based on a joint work with Tao Wang.