Relations between Lorentz-Zygmund and Grand Lebesgue Spaces and norms

TL;DR

This paper explores the relationships and embedding properties between Grand Lebesgue Spaces and Lorentz-Zygmund spaces, extending previous results and establishing the exactness of these embeddings.

Contribution

It introduces new embedding theorems between Grand Lebesgue and Lorentz-Zygmund spaces, improving upon prior results with precise estimates.

Findings

Established new embedding properties between the spaces.

Extended known results to more general spaces.

Proved the exactness of the embedding estimates.

Abstract

We establish imbedding properties between Grand Lebesgue Spaces and (generalized) Lorentz-Zygmund ones. We extend some known previous results concerning imbedding theorems between Grand Lebesgue and classical Lebesgue-Riesz spaces and we show the exactness of the obtained estimates.