Fourier tranform in exponential rearrangement invariant spaces

TL;DR

This paper studies Fourier series and transforms for functions in exponential Orlicz and other rearrangement invariant spaces on multi-dimensional domains, exploring their properties and behaviors.

Contribution

It introduces analysis of Fourier transforms within exponential Orlicz and rearrangement invariant spaces, expanding understanding of harmonic analysis in these function spaces.

Findings

Fourier series convergence properties in exponential Orlicz spaces

Behavior of Fourier transforms in rearrangement invariant spaces

Extensions of classical Fourier analysis results to new function spaces

Abstract

In this article we investigate the Fourier series and transforms for the functions defined on the $ [0, 2 \pi]^ d $ or $ R^d $ and belonging to the exponential Orlicz and some other rearrangement invariant (r.i.) spaces.