A conjecture of Antoni Zygmund

TL;DR

This paper proves an exponential covering theorem that confirms a long-standing conjecture by A. Zygmund from 1935, extending previous three-dimensional results to a more general setting.

Contribution

It introduces a new exponential covering theorem that resolves Zygmund's conjecture, advancing understanding in the field of harmonic analysis.

Findings

Confirmed Zygmund's conjecture from 1935

Extended three-dimensional results to higher dimensions

Established a new exponential covering theorem

Abstract

In this paper we establish an exponential covering theorem implying a conjecture formulated by A. Zygmund circa 1935 whose three-dimensional case was obtained by the first named author in 1978.