Person: Cobos Díaz, Fernando
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First Name
Fernando
Last Name
Cobos Díaz
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Análisis Matemático Matemática Aplicada
Area
Análisis Matemático
Identifiers
13 results
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Now showing 1 - 10 of 13
Item Measure of non-compactness and limiting interpolation with slowly varying functions(Banach Journal of Mathematical Analysis, 2024) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Grover, ManviWe give estimates for the measure of non-compactness of an operator interpolated by the limiting methods involving slowly varying functions. As applications we establish estimates for the measure of non-compactness of operators acting between Lorentz–Karamata spaces.Item Diversity of Lorentz-Zygmund spaces of operators defined by approximation numbers(Analysis Mathematica, 2023) Cobos Díaz, Fernando; Kühn, ThomasWe prove the following dichotomy for the spaces ℒ (a) p,q,α (X, Y) of all operators T ∈ ℒ(X, Y) whose approximation numbers belong to the Lorentz-Zygmund sequence spaces ℓp,q(log ℓ)α: If X and Y are infinite-dimensional Banach spaces, then the spaces ℒ (a) p,q,α (X, Y) with 0 < p < ∞, 0 < q ≤ ∞ and α ∈ ℝ are all different from each other, but otherwise, if X or Y are finite-dimensional, they are all equal (to ℒ(X, Y)). Moreover we show that the scale is strictly increasing in q, where ℒ (a) ∈,q (X, Y) is the space of all operators in ℒ(X, Y) whose approximation numbers are in the limiting Lorentz sequence space ∓∈,q.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 On a problem of Lions concerning real interpolation spaces. The quasi-Banach case(Journal of Mathematical Analysis and Applications, 2022) Cobos Díaz, Fernando; Cwikel, M.; Kühn, ThomasWe prove that, under a mild condition on a couple (A0;A1) of quasi-Banach spaces, all real interpolation spaces (A0;A1)θ,p with 0 < θ < 1 and 0 < p ≤ ∞ are different from each other. In the Banach case and for 1 ≤ p ≤ ∞ this was shown by Janson, Nilsson, Peetre and Zafran, thus solving an old problem posed by J.-L. Lions. Moreover, we give an application to certain spaces which are important objects in Operator Theory and which consist of bounded linear operators whose approximation numbers belong to Lorentz sequence spaces.Item On interpolation of weakly compact bilinear operators(Mathematische Nachrichten, 2022) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, AntónWe study the interpolation properties of weakly compact bilinear operators by the real method and also by the complex method. We also study the factorization property of weakly compact bilinear operators through reflexive Banach spaces.Item On the interpolation of the measure of non-compactness of bilinear operators with weak assumptions on the boundedness of the operator(Journal of Mathematical Analysis and Applications, 2021) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, AntónWe complete the range of the parameters in the interpolation formula established by Mastyło and Silva for the measure of non-compactness of a bilinear operator interpolated by the real method.Item Weakly compact bilinear operators among real interpolation spaces(Journal of Mathematical Analysis and Applications, 2022) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz MaríaWe show a necessary and sufficient condition for weak compactness of bilinear operators interpolated by the real method. This characterization does not hold for interpolated operators by the complex method.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 and applications to Besov spaces(Banach center publications, 2020) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz MaríaWe review several results on duality of logarithmic interpolation spaces and applications to Besov spaces. We also establish some new results on Besov spaces with smoothness close to zero defined by differences.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.