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

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.

References in corpus (3)

• Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
• Nikol'skii-type inequalities for rearrangement invariant spaces
• Bide - Side Exponential and Moment Inequalities for Tails of Distributions of Polynomial Martingales