1 citations · 1 across the 5 of their papers we have counts for
10 papers
Potential kernels for radial Dunkl Laplacians
Piotr Graczyk, Tomasz Luks, Patrice Sawyer
We derive two-sided bounds for the Newton and Poisson kernels of the -invariant Dunkl Laplacian in geometric complex case when the multiplicity , i.e. for flat complex s…
Multiple points of operator semistable Lévy processes
Tomasz Luks, Yimin Xiao
We determine the Hausdorff dimension of -multiple points for a symmetric operator semistable Lévy process in terms of the eigenvalues of its stabi…
On the Green function and Poisson integrals of the Dunkl Laplacian
Piotr Graczyk, Tomasz Luks, Margit Rösler
We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian in . As applications we derive the Poisson-Jensen for…
Space-time fractional Dirichlet problems
Boris Baeumer, Tomasz Luks, Mark M. Meerschaert
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an…
Hardy-Stein identities and square functions for semigroups
Rodrigo Bañuelos, Krzysztof Bogdan, Tomasz Luks
We prove a Hardy-Stein type identity for the semigroups of symmetric, pure-jump Lévy processes. Combined with the Burkholder-Gundy inequalities, it gives the two-way boundedn…
On the double points of operator stable Lévy processes
Tomasz Luks, Yimin Xiao
We determine the Hausdorff dimension of the set of double points for a symmetric operator stable Lévy process in terms of the eigenvalues of its stability exponent.