Fourier Series and Transforms in Grand Lebesgue Spaces As an particular case - exponential Orlicz spaces

TL;DR

This paper studies Fourier series and transforms within Grand Lebesgue Spaces and exponential Orlicz spaces, providing new estimates and examples to demonstrate their properties and applications.

Contribution

It introduces new results on Fourier analysis in Grand Lebesgue and exponential Orlicz spaces, including precise estimations and illustrative examples.

Findings

Derived estimates for Fourier series and transforms in Grand Lebesgue Spaces

Established results for Fourier transforms in exponential Orlicz spaces

Provided examples confirming the sharpness of the estimates

Abstract

In this article we investigate the Fourier series and transforms for the functions defined on the [-pi, pi]^ d or on the R^d and belonging to the (Bilateral) Grand Lebesgue Spaces. As a particular case we obtain some results about Fourier's transform in the so-called exponential Orlicz spaces. We construct also several examples to show the exactness of offered estimations.