Some remarks on extremal problems in weighted Bergman spaces of analytic functions

TL;DR

This paper investigates extremal distance problems in weighted Bergman spaces on the upper halfplane and bounded strictly pseudoconvex domains, providing sharp results that enhance understanding of function behavior in these complex spaces.

Contribution

It introduces new sharp extremal distance results for weighted Bergman spaces in both the upper halfplane and strictly pseudoconvex domains, extending previous work.

Findings

Sharp extremal distance results for weighted Bergman spaces on the upper halfplane

Extends extremal distance results to strictly pseudoconvex domains with smooth boundary

Provides new tools for analyzing function behavior in complex analysis

Abstract

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary