Gradient estimates of Dirichlet heat kernels for unimodal Levy processes

TL;DR

This paper derives gradient estimates for Dirichlet heat kernels associated with pure-jump isotropic unimodal Levy processes in multi-dimensional space, under mild conditions on the Levy measure and symbol.

Contribution

It provides new gradient estimates for heat kernels of Levy processes, extending understanding under less restrictive assumptions.

Findings

Gradient estimates are established for the heat kernels.

Results apply to a broad class of unimodal Levy processes.

The estimates improve previous bounds under mild assumptions.

Abstract

Under some mild assumptions on the Levy measure and the symbol we obtain gradient estimates of Dirichlet heat kernels for pure-jump isotropic unimodal Levy processes in $R^d$.