arXiv subjects

Marcin Gryszówka

Publications and source records attributed to Marcin Gryszówka.

3 recordsLinked to original sources

arXiv2024

$ε$-Approximability and Quantitative Fatou Property on Lipschitz-graph domains for a class of non-harmonic functions

We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are $ε$-approximable. As a consequence we obtain the quantitative Fatou theorem in the spirit of works e.g. by Garnett and Bortz-Hofmann. Such a class contains harmonic functions, as well as non-harmonic ones, for example nonnegative subharmonic functions, as illustrated by our discussion.

math.AP↗

arXiv2024

Carleson measures on domains in Heisenberg groups

We study the Carleson measures on NTA and ADP domains in the Heisenberg groups $\mathbb{H}^n$ and provide two characterizations of such measures: (1) in terms of the level sets of subelliptic harmonic functions and (2) via the $1$-quasiconformal family of mappings on the Korányi--Reimann unit ball. Moreover, we establish the $L^2$-bounds for the square function $S_α$ of a subelliptic harmonic function and the Carleson measure estimates for the BMO boundary data, both on NTA domains in $\mathbb{H}^n$. Finally, we prove a Fatou-type theorem on $(ε, δ)$-domains in $\mathbb{H}^n$.

math.AP↗

arXiv2023

$\varepsilon$-approximability and Quantitative Fatou Theorem on Riemannian Manifolds

We prove the Quantitative Fatou Theorem for Lipschitz domains on complete Riemannian manifolds. This requires extending the $\varepsilon$-approximation lemma to the manifold setting. Our studies apply to harmonic functions, as well as to a class of A-harmonic functions on manifolds. The presented results extend works by Dahlberg, Garnett, Bortz and Hofmann.

math.AP↗