On balayage and B-balayage operators

TL;DR

This paper explores the properties of balayage and B-balayage operators within Hardy and Bergman spaces, extending existing theoretical results to deepen understanding of these operators in complex analysis.

Contribution

It extends known results on balayage and B-balayage operators, providing new insights into their behavior in Hardy and Bergman spaces.

Findings

Extended the theoretical framework of balayage operators in Hardy spaces.

Analyzed the B-balayage operators in Bergman spaces.

Provided new bounds and properties for these operators.

Abstract

Here we consider the balayage operator in the setting of $H^p$ spaces and its Bergman space version (B-balayage) introduced by H. Wulan, J. Yang and K. Zhu \cite{WYZ}, and extend some known results on these operators.