On the Moser-Trudinger inequality in complex space

TL;DR

This paper establishes a complex space analogue of the Moser-Trudinger and Sobolev inequalities, providing new bounds for plurisubharmonic functions with finite pluricomplex energy.

Contribution

It introduces the pluricomplex version of these inequalities and estimates the associated constants, extending classical inequalities to complex analysis.

Findings

Proved the pluricomplex Moser-Trudinger inequality.

Derived bounds for the constants involved.

Extended classical inequalities to complex space context.

Abstract

In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions with finite pluricomplex energy, and we estimate the concerned constants.