External area integral inequality for the Cauchy-Leray-Fantappi\'e integral

TL;DR

This paper extends the Luzin inequality to functions defined by the Cauchy-Leray-Fantappié integral outside convex domains in complex spaces, advancing mathematical understanding of integral inequalities.

Contribution

It introduces a new inequality for the Cauchy-Leray-Fantappié integral on convex domain complements, expanding existing theoretical frameworks.

Findings

Extended Luzin inequality for complex integrals

Applicable to convex domain complements in complex space

Provides new tools for complex analysis

Abstract

In this paper we extend Luzin inequality for functions deined by the Cauchy-Leray-Fantappi\'e integral on the complement of a convex domain in $\mathbb{C}^n$. The work is supported by Russian Science Foundation Grant 14-41-00010.