Some properties of plurisubharmonic functions

TL;DR

This paper proves two properties of plurisubharmonic functions: a Skoda type integrability theorem with Monge-Ampère mass and a local Lipschitz regularity outside small measure sets.

Contribution

It introduces a Skoda type integrability result for p.s.h. functions with H"older continuous potentials and establishes local Lipschitz regularity outside measure-controlled sets.

Findings

Proved a Skoda type integrability theorem for p.s.h. functions.

Established local k-Lipschitz regularity outside small measure sets.

Demonstrated properties under Monge-Ampère mass with H"older continuous potential.

Abstract

Two properties of plurisubharmonic functions are proven. The first result is a Skoda type integrability theorem with respect to a Monge-Amp\`ere mass with H\"older continuous potential. The second one says that locally, a p.s.h. function is $k$-Lipschitz outside a set of Lebesgue measure smaller that $c/k^2$.