Person:
Fernández Besoy, Blanca

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First Name
Blanca
Last Name
Fernández Besoy
URI
https://hdl.handle.net/20.500.14352/87004
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Análisis Matemático Matemática Aplicada
Area
Análisis Matemático
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2019 - 201912020 - 20222
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Item Type: Publication × Subject: 517.98 ×

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Now showing 1 - 3 of 3
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    On function spaces of Lorentz–Sobolev type
    (Mathematische Annalen, 2021) Fernández Besoy, Blanca; Cobos Díaz, Fernando; Triebel, Hans
    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.
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    Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications
    (Journal of Functional Analysis, 2022) Fernández Besoy, Blanca; Cobos Díaz, Fernando
    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.
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    Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces
    (Journal of Approximation Theory, 2019) Fernández Besoy, Blanca; Cobos Díaz, Fernando
    Working in the setting of quasi-Banach couples, we establish a formula for the measure of non-compactness of bilinear operators interpolated by the general real method. The result applies to the real method and to the real method with a function parameter.