Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications

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Besoy, Blanca F. and Cobos, Fernando (2022) Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications. Journal of Functional Analysis . p. 109452. ISSN 0022-1236

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Official URL: https://doi.org/10.1016/j.jfa.2022.109452




Abstract

We establish atomic decompositions and characterizations in terms of wavelets for Besov-Lorentz spaces Bsq Lp,r (Rn) and for Triebel-Lizorkin-Lorentz spaces Fsq Lp,r (Rn) in the whole range of parameters. As application we obtain new interpolation formulae between spaces of Lorentz-Sobolev type. We also remove the restrictions on the parameters in a result of Peetre on optimal embeddings of Besov spaces. Moreover, we derive results on diffeomorphisms, extension operators and multipliers for Bsq Lp,∞ (Rn). Finally, we describe Bsq Lp,r (Rn) as an approximation space, which allows us to show new sufficient conditions on parameters for Bsq Lp,r (Rn) to be a multiplication algebra.


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

Uncontrolled Keywords:Besov-Lorentz spaces; Triebel-Lizorkin-Lorentz spaces; Approximation spaces; Multiplication algebras
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:71219
Deposited On:14 Mar 2022 18:58
Last Modified:20 Oct 2022 15:59

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