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. |
|