Translator Disclaimer
December 2013 Absolutely continuous embeddings between spaces of functions
Pedro Fernández-Martínez, Antonio Manzano
Funct. Approx. Comment. Math. 49(2): 303-320 (December 2013). DOI: 10.7169/facm/2013.49.2.9

Abstract

Absolute continuity of an embedding between Banach function spaces is an interesting property which is closely related to compactness. In this paper we study absolutely continuous embeddings between arbitrary Banach spaces intermediate with respect to the couple $(L_{1}(\Omega), L_{\infty}(\Omega))$. Our results allow to check if an embedding of such spaces is absolutely continuous. Applications related with the degree of proximity between two function spaces are established for the case $\Omega=[0,1]$ and $\Omega=[0,\infty)$.

Citation

Download Citation

Pedro Fernández-Martínez. Antonio Manzano. "Absolutely continuous embeddings between spaces of functions." Funct. Approx. Comment. Math. 49 (2) 303 - 320, December 2013. https://doi.org/10.7169/facm/2013.49.2.9

Information

Published: December 2013
First available in Project Euclid: 20 December 2013

zbMATH: 1290.46023
MathSciNet: MR3161498
Digital Object Identifier: 10.7169/facm/2013.49.2.9

Subjects:
Primary: 46E30
Secondary: 46B42, 46B70

Rights: Copyright © 2013 Adam Mickiewicz University

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.49 • No. 2 • December 2013
Back to Top