Gradient estimates for the fundamental solution of Lévy type operator

Abstract

We prove a gradient estimate and the Hölder continuity of the gradient for the fundamental solution of a class of α-stable type operators with α ∈ (0, 1), which improve known results in the literature where the condition α > 1/2 is commonly assumed.

Keywords

• lévy type operator
• heat kernel estimate
• gradient estimate
• stochastic differential equations
• primary 60j35
• 60h15
• 60j75
• secondary 60j45