T. Luks

activity

20092019

most citedHarmonic Hardy spaces on smooth domains

1 citations · 1 across the 5 of their papers we have counts for

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math.AP2019

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 $W$ -invariant Dunkl Laplacian in geometric complex case when the multiplicity $k (α) = 1$ , i.e. for flat complex s…

math.AP2016

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 $Δ_{k}$ in $R^{d}$ . As applications we derive the Poisson-Jensen for…

math.AP2012

Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Piotr Graczyk, Tomasz Jakubowski, Tomasz Luks

Let $L = Δ^{α /2} + b \cdot \nabla$ with $α \in (1, 2)$ . We prove the Martin representation and the Relative Fatou Theorem for non-negative singular $L$ -harmonic functions on ${\mathcal C}^…

math.AP2009★ 1 cited

Harmonic Hardy spaces on smooth domains

Tomasz Luks

The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.