Functiones et Approximatio Commentarii Mathematici

Absolutely continuous embeddings between spaces of functions

Pedro Fernández-Martínez and Antonio Manzano

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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 $\Omega=[0,\infty)$.

Article information

Source
Funct. Approx. Comment. Math., Volume 49, Number 2 (2013), 303-320.

Dates
First available in Project Euclid: 20 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1387572234

Digital Object Identifier
doi:10.7169/facm/2013.49.2.9

Mathematical Reviews number (MathSciNet)
MR3161498

Zentralblatt MATH identifier
1290.46023

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46B70: Interpolation between normed linear spaces [See also 46M35] 46B42: Banach lattices [See also 46A40, 46B40]

Keywords
absolutely continuous embedding interpolation quasiconcave function Banach lattice proximity between function spaces

Citation

Fernández-Martínez, Pedro; Manzano, Antonio. Absolutely continuous embeddings between spaces of functions. Funct. Approx. Comment. Math. 49 (2013), no. 2, 303--320. doi:10.7169/facm/2013.49.2.9. https://projecteuclid.org/euclid.facm/1387572234


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