Uniform Boundary Harnack Principle for Rotationally Symmetric Levy processes in General Open Sets

TL;DR

This paper establishes a uniform boundary Harnack principle for harmonic functions related to a broad class of rotationally symmetric purely discontinuous Lévy processes in general open sets, extending existing theoretical frameworks.

Contribution

It introduces a new uniform boundary Harnack principle applicable to a wide class of rotationally symmetric Lévy processes in arbitrary open sets.

Findings

Proves the boundary Harnack principle for these processes.

Extends the principle to general open sets.

Provides theoretical foundation for further analysis of Lévy processes.

Abstract

In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous L\'evy processes.