Person: Fernández Besoy, Blanca
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First Name
Blanca
Last Name
Fernández Besoy
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Análisis Matemático Matemática Aplicada
Area
Análisis Matemático
Identifiers
7 results
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Item Logarithmic interpolation methods, measure of non-compactness of bilinear operators and function spaces of Lorentz-Sobolev type(2021) Fernández Besoy, Blanca; Cobos Díaz, FernandoThe guiding theme and main topic of this monograph is Interpolation Theory. However, as it is suggested by the title, we can distinguish three different parts: the first one covers Chapters 3‐7 and it focuses on the study of the so‐called logarithmic interpolation methods. As for the second one, it consists of Chapter 8 and concentrates on the research of some properties related to the interpolation of bilinear operators, this time by the real method and some of its variants. Finally, the third part, containing Chapters 9 and 10, examines function spaces of Lorentz‐Sobolev type, in particular, Besov‐Lorentz and Triebel‐Lizorkin‐Lorentz spaces and it studies some of its properties by means of different interpolation results.Interpolation Theory is a branch of Functional Analysis with important applications to Partial Differential Equations, Harmonic Analysis, Approximation Theory, Function Spaces and Operators Theory, among other areas in mathematics. Reference sources for the subject are, for example, the books by Bennett and Sharpley [6], Bergh and Löfström [11], Butzer and Berens [23], Brudnyĭ and Krugljak [22], König [84] and Triebel [110]...Item Logarithmic interpolation methods and measure of non-compactness(Quarterly Journal of Mathematics, 2019) Cobos Díaz, Fernando; Fernández Besoy, BlancaWe derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with θ = 0, 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.Item On function spaces of Lorentz–Sobolev type(Mathematische Annalen, 2021) Fernández Besoy, Blanca; Cobos Díaz, Fernando; Triebel, HansWe 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.Item The equivalence theorem for logarithmic interpolation spaces in the quasi-Banach case(Zeitschrift für Analysis und ihre Anwendungen, 2020) Cobos Díaz, Fernando; Fernández Besoy, BlancaWe study the description by means of the J-functional of logarithmic interpolation spaces (A0, A1) 1, q, A in the category of the p-normed quasi-Banach couples (0 < p ≤ 1). When (A0, A1) is a Banach couple, it is known that the description changes depending on the relationship between q and A. In our more general setting, the parameter p also has an important role as the results show.Item Duality for logarithmic interpolation spaces when 0 < q < 1 and applications(Journal of Mathematical Analysis and Applications, 2018) Cobos Díaz, Fernando; Fernández Besoy, BlancaWe work with spaces (A0;A1)θ;q;A which are logarithmic perturbations of the real interpolation spaces. We determine the dual of (A0;A1)θ;q;A when0 < q < 1. As we show, if θ = 0 or 1 then the dual space depends on the relationship between q and A. Furthermore we apply the abstract results to compute the dual space of Besov spaces of logarithmic smoothness and the dual space of spaces of compact operators in a Hilbert space which are closeto the Macaev ideals.Item 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, FernandoWe 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 Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces(Journal of Approximation Theory, 2019) Fernández Besoy, Blanca; Cobos Díaz, FernandoWorking 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.