Functiones et Approximatio Commentarii Mathematici

Absolutely continuous embeddings between spaces of functions

Pedro Fernández-Martínez and Antonio Manzano

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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

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

First available in Project Euclid: 20 December 2013

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Zentralblatt MATH identifier

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]

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


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.

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