We prove gradient estimates for harmonic functions with respect to a $ d $-dimensional
unimodal pure-jump Lévy process under some mild assumptions on the density of its Lévy …

We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators.
The extension is given by a suitable Poisson integral and solves the corresponding nonlocal …

Barriers, exit time and survival probability for unimodal Lévy processes | Probability Theory
and Related Fields Skip to main content SpringerLink Log in Menu Find a journal Publish with …

In this paper we discuss non-local operators with killing potentials, which may not be in the
standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric …

Estimates of transition densities and their derivatives for jump Lévy processes - ScienceDirect
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In this paper, we study the following stochastic differential equation (SDE) in Rd: dXt= dZt+ b
(t, Xt) dt, X0= x, where Z is a Lévy process. We show that for a large class of Lévy processes …

Dirichlet heat kernel for unimodal Lévy processes - ScienceDirect Skip to main contentSkip
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arXiv:1412.7717v2 [math.AP] 28 Dec 2014 Page 1 arXiv:1412.7717v2 [math.AP] 28 Dec 2014
HARDY INEQUALITIES AND NON-EXPLOSION RESULTS FOR SEMIGROUPS KRZYSZTOF …

Due to the increasing power of modern computers, it has become ever more popular to use
sophisticated models to describe the irregular behaviour of real life phenomena. Nowadays …

In this paper, we present an-regularity theory for parabolic equations of the form Here,
represents anisotropic nonlocal operators encompassing the singular anisotropic fractional …