Characterizing Sobolev spaces of vector-valued functions

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Caamaño Aldemunde, Iván and Jaramillo Aguado, Jesús Ángel and Prieto Yerro, M. Ángeles (2022) Characterizing Sobolev spaces of vector-valued functions. Journal of Mathematical Analysis and Applications, 514 (1). p. 126250. ISSN 0022-247X

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Official URL: https://doi.org/10.1016/j.jmaa.2022.126250




Abstract

We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Ω⊂RN and a Banach space V, we characterize the functions in the Sobolev-Reshetnyak space R1,p(Ω, V), where 1 ≤p≤∞, in terms of the existence of partial metric derivatives or partial w∗-derivatives with suitable integrability properties. In the case p=∞ the Sobolev-Reshetnyak space R1,∞(Ω, V)is characterized in terms of a uniform local Lipschitz property. We also consider the special case of the space V=l∞.


Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Sobolev spaces; Vector-valued functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:72016
Deposited On:03 May 2022 14:04
Last Modified:02 Jun 2022 15:57

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