Symmetry and functional inequalities for stable Lévy-type operators

Lu-Jing Huang and Tao Wang

Stochastic Processes and their Applications, 2025, vol. 183, issue C

Abstract: In this paper, we establish the sufficient and necessary conditions for the symmetry of the following stable Lévy-type operator L on R: L=a(x)Δα/2+b(x)ddx,where a is a continuous and strictly positive function, and b is a differentiable function. We then study the criteria for functional inequalities, such as logarithmic Sobolev inequalities, Nash inequalities and super-Poincaré inequalities under the assumption of symmetry. Our approach involves the Orlicz space theory and the estimates of the Green functions.

Keywords: Stable Lévy-type operator; Symmetry; Functional inequality; Orlicz space; Green function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104600

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