Growth description of $p$th means of the Green potential in the unit ball

TL;DR

This paper investigates how the $p$th means of the invariant Green potential grow in the unit ball of complex space, linking growth rates to measure smoothness and extending previous boundedness results.

Contribution

It provides a new criterion for the boundedness of $p$th means of the Green potential, generalizing M. Stoll's earlier results.

Findings

Derived growth estimates for $p$th means in terms of measure smoothness

Established a criterion for boundedness of $p$th means

Generalized previous results by M. Stoll

Abstract

We describe the growth of $p$th means, $1<p<\frac{2n-1}{2(n-1)}$, of the invariant Green potential in the unit ball in $\mathbb{C}^n$ in terms of smoothness properties of a measure. In particular, a criterion of boundedness of $p$th means of the potential is obtained, a result of M. Stoll is generalized.