On function spaces of Lorentz–Sobolev type

We work with Triebel–Lizorkin spaces FsqLp,r(Rn) and Besov spaces BsqLp,r(Rn) with Lorentz smoothness. Using their characterizations by real interpolation we show how to transfer a number of properties of the usual Triebel–Lizorkin and Besov spaces to the spaces with Lorentz smoothness. In particula...

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Bibliographic Details
Authors: Fernández Besoy, Blanca, Cobos Díaz, Fernando, Triebel, Hans
Format: article
Publication Date:2021
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/7997
Online Access:https://hdl.handle.net/20.500.14352/7997
Access Level:Open access
Keyword:517.98
517.982.2
Triebel-Lizorkin-Lorentz spaces
Besov-Lorentz spaces
Real interpolation
Multiplications
Análisis funcional y teoría de operadores
Description
Summary:We work with Triebel–Lizorkin spaces FsqLp,r(Rn) and Besov spaces BsqLp,r(Rn) with Lorentz smoothness. Using their characterizations by real interpolation we show how to transfer a number of properties of the usual Triebel–Lizorkin and Besov spaces to the spaces with Lorentz smoothness. In particular, we give results on diffeomorphisms, extension operators, multipliers and we also show sufficient conditions on parameters for FsqLp,r(Rn) and BsqLp,r(Rn) to be multiplication algebras.