Axler-Zheng type theorem on a class of domains in C^n

TL;DR

This paper extends the Axler-Zheng theorem to smooth bounded pseudoconvex domains in complex n-space where the dbar-Neumann operator is compact, broadening the theorem's applicability in several complex variables.

Contribution

It establishes a version of Axler-Zheng's Theorem for a new class of domains in C^n with compact dbar-Neumann operators, advancing the understanding of function theory in several complex variables.

Findings

Proves Axler-Zheng type theorem on smooth bounded pseudoconvex domains in C^n.

Shows the theorem holds when the dbar-Neumann operator is compact.

Expands the class of domains where the Axler-Zheng theorem applies.

Abstract

We prove a version of Axler-Zheng's Theorem on smooth bounded pseudoconvex domains in C^n on which the dbar-Neumann operator is compact.