Regularity of fundamental solutions for Lévy-type operators
Volume 71 / 2023
Bulletin Polish Acad. Sci. Math. 71 (2023), 169-191
MSC: Primary 60J35; Secondary 47G20, 47D03.
DOI: 10.4064/ba230424-12-9
Published online: 8 November 2023
Abstract
For a class of non-symmetric non-local Lévy-type operators $\mathcal L^{\kappa}$, which include those of the form $$ \mathcal L^{\kappa}f(x):= \int _{\mathbb R^d}( f(x+z)-f(x)- \mathbf 1_{|z| \lt 1} \langle z,\nabla f(x)\rangle )\kappa (x,z)J(z)\, dz, $$ we prove regularity of the fundamental solution $p^{\kappa }$ to the equation $\partial _t =\mathcal L^{\kappa}$.
