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Autor Cobos, Fernando |
Documentos disponibles escritos por este autor (121)
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Besoy, Blanca F. ; Cobos, Fernando | 2019We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with ? = 0, 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.![]()
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Besoy, Blanca F. ; Cobos, Fernando | 2020We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with [?] = 0; 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.![]()
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This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value p[...]![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Manzano, Antonio ; Martínez, Antón | Heldermann Verlag | 2007Let A0 and A1 be quasi-Banach spaces with A0 ,! A1. By means of a direct approach, we show that the interpolation spaces on (A0;A1) generated by the function parameter tµ(1 + j log tj)¡b can be expressed in terms of classical real inter-polation[...]![]()
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We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces![]()
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We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces.![]()
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We establish an estimate for the measure of non-compactness of an interpolated operator acting from a J-space into a K-space. Our result refers to general Banach N-tuples. We also derive estimates for entropy numbers if some of the N-tuples redu[...]![]()
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We establish formulae for the measure of non-compactness of operators interpolated by limiting methods that come up by the choice ?=0 and ?=1 in the definition of the real method.![]()
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The authors consider multiparameter scales of interpolation spaces and prove a general form of the Wolff reiteration theorem [cf. T. H. Wolff, Lecture Notes Math. 908, 199- 204 (1982)] for n- tuples of Banach spaces. The proof, based on the use [...]![]()
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We give some new examples of bounded multilinear forms on th Hilbert spaces 2 and L2(0,?). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m ? 3) on 2 which can be regarded as the multilinear[...]![]()
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We study interpolation methods associated to polygons and establish estimates for the norms of interpolated operators. Our results explain the geometrical base of estimates in the literature. Applications to interpolation of weighted L(p)-spaces[...]![]()
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Let d ? N and let ? be a bounded Lipschitz domain in Rd. We prove that the embedding Id : Bd (?) ?? L (log L) (?) is nuclear if a![]()
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Cobos, Fernando ; Fernandez-Cabrera, Luz ; Kuehn, Thomas ; Ullrich, Tino | Academic Press-Elsevier Science | 2009We investigate the limit class of interpolation spaces that comes up by the choice ? = 0 in the definition of the real method. These spaces arise naturally interpolating by the J -method associated to the unit square. Their duals coincide with t[...]![]()
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Working on the d-torus, we show that Besov spaces Bps(Lp(logL)a) modelled on Zygmund spaces can be described in terms of classical Besov spaces. Several other properties of spaces Bps(Lp(logL)a) are also established. In particular, in the critic[...]![]()
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We compare Besov spaces B-p,q(0,b) with zero classical smoothness and logarithmic smoothness b defined by using the Fourier transform with the corresponding spaces:B-p,q(0,b) defined by means of the modulus of smoothness. In particular, we show [...]![]()
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Let ? = (A? , A?) , B? = (B? , B?) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ||T(a, b)||? ? M[sub]j ||a||?[sub]j ||b||?[sub]j for a ? A? ? A?, b ? B? ? B?, j = 0, 1. If T : A°[sub]j × B°[sub]j ?? E com[...]![]()
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Let H denote a Hilbert space, T a compact operator on H, {sn(T)}1 n=1 the eigenvalues of |T|, and Sp (p > 0) the set of all such T for which {sn(T)}1 n=1 is in `p. If A and B are bounded linear operators on L2, say that B pointwise dominates A [...]![]()
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Cobos, Fernando ; Fernández-Martínez, Pedro ; Martínez, Antón ; Raynaud, Yves | Cambridge Univ Press | 1999We study the relationship between the dual of the #C-space defined by means of a polygon and the /-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is f[...]![]()
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In a previous paper, the authors laid the foundations of a theory of Schatten±von Neumann classes 'p (0!p%¢) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional case, it is shown that the best constant d[...]![]()
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We show a direct proof for the generalized Hardy’s inequality obtained by the first author Math. Nachr. 126, 281-300, 1986. Our techniques are elementary and work in the limit case which was not covered in [loc. cit.]. Some applications to eigen[...]![]()
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We determine the smallest Schatten class containing all integral operators with kernels in L(p)(L(p',q))symm, where 2![]()
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We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Gauthier-Villars/Editions Elsevier | 2006We show a necessary and sufficient condition on the lattice ? for the general real method (· , ·)? to preserve the Banach-algebra structure. As an application we derive factorization of weakly compact homomorphisms through interpolation properti[...]![]()
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The authors investigate the behaviour of bilinear operators under interpolation by the methods associated to polygons. These methods, working with N-tuples (N _ 3) of Banach spaces instead of couples, were introduced by F. Cobos and J. Peetre [P[...]![]()
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We prove that the classical Lions-Peetre compactness theorems for linear operators still hold for Lipschitz operators. As a consequence, we deduce that certain Uryson integral operators are compact. We also show that Lipschitz operators can be i[...]![]()
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The authors extend a result of K. Hayakawa [J. Math. Soc. Jap. 21, 189-199 (1969; Zbl 0181.137)], and prove: If T is a linear operator such that T: A0 ! B0, is bounded,and T: A1 ! B1 is compact, and moreover, A1 A0, then T: ¯ A,q ! ¯B,q is comp[...]![]()
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We describe the spaces obtained by applying the interpolation methods associated to polygons to N-tuples of weighted Lp-spaces, N-tuples of classical Lorentz spaces and some other N-tuples of function spaces.![]()
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We improve the known results on interpolation of strictly singular operators and strictly co-singular operators in several directions. Applications are given to embeddings between symmetric spaces.![]()
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We revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.![]()
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We describe the behaviour under interpolation of a limit class of approximation spaces. We characterize them as extrapolation spaces. Moreover, we study the boundedness of certain operators on these spaces. As an application, we derive several r[...]![]()
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Cobos, Fernando ; Domínguez, Oscar ; Kühn, Thomas | 2018Let Bp,qs,?(?) be the Besov space with classical smoothness s and additional logarithmic smoothness of order ? on a bounded Lipschitz domain ? in Rd. For s1, s2 ? R, 1 ? p1, p2, q1, q2 ? ? and s1 ? s2 = d ? d(1/p2 ? 1/p1)+, we show a su?cient co[...]![]()
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We work with spaces of periodic functions on the d-dimensional torus. We show that estimates for L?-approximation of Sobolev functions remain valid when we replace L1 by the isotropic periodic Besov space B01;1 or the periodic Besovspace with do[...]![]()
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We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.![]()
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We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.![]()
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This article deals with K- and J-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compac[...]![]()
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We establish interpolation formulae for operator spaces that are components of a given quasi-normed operator ideal.![]()
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The authors prove a representation theorem in terms of finite rank operators for operators´T on Banach spaces which satisfy sup n2N (log n) an(T)![]()
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Let E be a Banach function lattice such that L1[0; 1] ,! E ,! L1[0; 1]. We characterize the strict singularity of the embedding L1[0; 1] ,! E and the strict cosingularity of E ,! L1[0; 1] in terms of functionals de_ned by using characteristic fu[...]![]()
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We describe a new approach to interpolate by the complex method quasi-Banach couples formed by real-intermediate spaces. End-point cases are also considered, and applications are given to function spaces and to operator spaces.![]()
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We improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.![]()
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Compactness results of Cobos and Peetre [3] guarantee that the interpolated operator is compact assuming that all but two restrictions of the operator (located in adjacent vertices) are compact. Comparing these results with others in the literat[...]![]()
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On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators
We show that if the general real method (. , .)(Gamma) preserves the Banach-algebra Structure, then a bilinear interpolation theorem holds for (. , .)(Gamma).![]()
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Using limiting interpolation techniques we study the elationship between Besov spaces B0,?1/q p,q with zero classical smoothness and logarithmic smoothness ?1/q defined by means of differences with similar spaces 0,b,d p,q defined by means of th[...]![]()
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We show that if the duality between a Banach space A and its anti-dual A* is given by the inner product of a Hilbert space H, then (A, A*)1/2,2 = H = (A,A*)[l,2~, provided A satisfies certain mild conditions. We do not assume A is reflexive. App[...]![]()
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Interpolating compactness properties of operators is a long standing and important problem. In this paper, the authors consider the problem in a very general setting of Aronszajn-Gagliardo functors. In simplest terms they show that if T : A0 ! B[...]