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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2017 Volume 102, Issue 5, Pages 736–748 (Mi mzm11778)

This article is cited in 6 papers

Embeddings between Grand, Small, and Variable Lebesgue Spaces

D. Cruz-Uribea, A. Fiorenzabc, O. M. Guzmand

a University of Alabama at Tuscaloosa, USA
b Istituto per le Applicazioni del Calcolo "Mauro Picone"
c Universitá degli Studi di Napoli Federico II
d Universidad Nacional de Colombia

Abstract: We give conditions on the exponent function $p(\,\cdot\,)$ that imply the existence of embeddings between the grand, small, and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent results by the second author, Rakotoson and Sbordone.

Keywords: Banach function spaces, variable Lebesgue spaces, grand Lebesgue spaces, small Lebesgue spaces, embeddings.

UDC: 517

Received: 10.04.2017
Revised: 23.06.2017

DOI: 10.4213/mzm11778


 English version:
Mathematical Notes, 2017, 102:5, 677–686

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© Steklov Math. Inst. of RAS, 2024