2022•arXiv (Cornell University)Open access

Relations between Lorentz-Zygmund and Grand Lebesgue Spaces and norms

Maria Rosaria Formica, Eugeny Ostrovsky, L. Sirota

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.

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Key concepts: Lp space, Lebesgue's number lemma, Lorentz transformation, Lebesgue integration, Mathematics, Pure mathematics, Singular integral operators of convolution type, Lebesgue–Stieltjes integration