$p$-Summable commutators in Bergman spaces on egg domains

TL;DR

This paper determines the specific values of p for which polynomial multiplication operators on Bergman spaces over complex ellipsoids are Schatten p-summable, advancing understanding of operator theory in complex analysis.

Contribution

It precisely characterizes the range of p for Schatten p-summability of polynomial multiplication operators on Bergman spaces over egg domains.

Findings

Identifies the exact p-range for Schatten p-summability.

Provides new insights into operator behavior on complex ellipsoid domains.

Enhances understanding of function space operators in several complex variables.

Abstract

The exact range of the positive real parameter $p$ is determined so that the multiplications by polynomial functions acting on Bergman spaces over complex ellipsoids are Schatten $p$-summable.