Trigonometric approximation in Sobolev-Grand Lebesgue Spaces

TL;DR

This paper explores the theory of trigonometric approximation within Sobolev-Grand Lebesgue Spaces, a class of Banach spaces that combine properties of Sobolev and Grand Lebesgue spaces, advancing the understanding of approximation in these complex function spaces.

Contribution

It introduces the framework for trigonometric approximation in Sobolev-Grand Lebesgue Spaces, extending classical approximation theory to new functional settings.

Findings

Established approximation bounds in Sobolev-Grand Lebesgue Spaces

Extended classical approximation results to these new spaces

Provided foundational results for further research in approximation theory

Abstract

We study in this short preprint the theory of trigonometric approximation in the so-called Banach functional rearrangement invariant Sobolev-Grand Lebesgue Spaces.