The unconditional case of the complex S-inequality

TL;DR

This paper proves the complex S-inequality for complete Reinhardt sets, establishing that it also holds for unconditional convex sets, thereby extending the inequality's applicability in complex analysis.

Contribution

It introduces the complex counterpart of the S-inequality for complete Reinhardt sets, demonstrating its validity for unconditional convex sets.

Findings

Proves the complex S-inequality for complete Reinhardt sets

Shows the inequality holds for unconditional convex sets

Extends the scope of the S-inequality in complex analysis

Abstract

In this note we prove the complex counterpart of the S-inequality for complete Reinhardt sets. In particular, this result implies that the complex S-inequality holds for unconditional convex sets.