Some remarks on the Cegrell's class $\mathcal{F}$

TL;DR

This paper investigates the boundary behavior of functions in Cegrell's class within strictly pseudoconvex domains and proposes a new condition for membership in this class in the unit ball.

Contribution

It provides new insights into the boundary behavior of functions in Cegrell's class and introduces a sufficient condition for membership in the class in the unit ball.

Findings

Characterization of near-boundary behavior in strictly pseudoconvex domains

A new sufficient condition for belonging to Cegrell's class in the unit ball

Enhanced understanding of function classes in complex analysis

Abstract

In this paper, we study the near-boundary behavior of functions $u\in\mathcal{F}(\Omega)$ in the case where $\Omega$ is strictly pseudoconvex. We also introduce a sufficient condition for belonging to $\mathcal{F}$ in the case where $\Omega$ is the unit ball.