A uniform boundedness principle in pluripotential theory

TL;DR

This paper establishes a local uniform boundedness principle in pluripotential theory, demonstrating that separate boundedness above for families of continuous plurisubharmonic functions implies joint boundedness.

Contribution

It introduces a new uniform boundedness principle specific to pluripotential theory, extending classical ideas to this complex analysis context.

Findings

Separate boundedness above implies joint boundedness locally.

The result applies to families of continuous plurisubharmonic functions.

Provides a foundational tool for further pluripotential analysis.

Abstract

For families of continuous plurisubharmonic functions we show that, in a local sense, separately bounded above implies bounded above.