Work

ɛ-approximability and quantitative Fatou property on Lipschitz-graph domains for a class of non-harmonic functions

Year: 2026

Type: article

Abstract: We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are $\varepsilon$ -approximable. As a consequence, we obtain the quantitative Fatou theorem in the spirit of works, for example, by Garnett [6] and Bortz–Hofmann [1]. Such a class contains harmonic functions, as well as non-harmonic ones, for example, nonnegative subharmonic functions whose gradient norm is quasi-nearly subharmonic, as illustrated by our discussion.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2026.10138

Authors: Tomasz Adamowicz, María J. González, Marcin Gryszówka

Institutions: Institute of Mathematics, Polish Academy of Sciences, Universidad de Cádiz, University of Warsaw

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

OpenAlex ID: W7143595945

FWCI:

Cites: 16

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