Información del autor
Autor Cobos, Fernando |
Documentos disponibles escritos por este autor (121)
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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[...]