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Autor Cobos, Fernando |
Documentos disponibles escritos por este autor (121)
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A procedure is given to reduce the interpolation spaces on an ordered pair generated by the function parameter t? (1 + |log t|)?b to the classical real interpolation spaces. Applications are given for Lorentz–Zygmund function spaces, Besov space[...]![]()
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We establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice ?. The formula is given in terms of the norms of the shift operators in ?.![]()
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We investigate the limit J-spaces corresponding to the general real method. These interpolation spaces are defined by Banach sequence lattices and include those spaces that arise by the choice ? = 0 in the definition of the real method. We pay e[...]![]()
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With the help of limiting interpolation we determine the spaces obtained by iteration of approximation constructions. Then we apply the reiteration formula and limiting interpolation to investigate several problems on Besov spaces, including emb[...]![]()
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Besoy, Blanca F. ; Cobos, Fernando | 2019We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-ato[...]![]()
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We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-ato[...]![]()
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If T : A0 ! B boundedly and T : A1 ! B compactly, then a result of Lions{Peetre shows that T : A ! B compactly for a certain class of spaces A which are intermediate with respect to A0 and A1. We investigate to what extent such results can hold [...]![]()
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We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We als[...]![]()
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Let ? be a bounded domain in Rn and denote by id? the restriction operator from the Besov space B1+n/p pq (Rn) into the generalized Lipschitz space Lip(1,??)(?). We study the sequence of entropy numbers of this operator and prove that, up to log[...]![]()
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We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Polish Acad Sciencies Inst Mathematics | 2005The paper establishes necessary and sufficient conditions for compactness of operators acting between general K -spaces, general J -spaces and operators acting from a J -space into a K -space. Applications to interpolation of compact operators a[...]![]()
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We establish a compactness interpolation result for bilinear operators of the type proved by Janson for bounded bilinear operators. We also give an application to compactness of convolution operators.![]()
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We characterize compact operators between complex interpolation spaces and between spaces obtained by using certain minimal methods in the sense of Aronszajn and Gagliardo. Applications to interpolation of compact operators are also given.![]()
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A theorem due to S. Janson, P. Nilsson, J. Peetre and M. Zafran [Proc. Lond. Math. Soc., III. Ser. 48, 283-299 (1984; Zbl 0532.46046)] states that for a Banach couple A such that _(A) is not closed in _(A) the real interpolation spaces A_,q and [...]![]()
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We work with logarithmic interpolation methods (A0,A1)?,q,A where ?=0 or 1. On the contrary to the case 0![]()
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Let S,q be the collection of all compact operators T on a (complex) Hilbert space H such that (INVALID INPUT),q(T) = (P1 n=1((n)sn(T))qn?1)1/q![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. | 2020We 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.![]()
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We work with spaces (A0;A1)?;q;A which are logarithmic perturbations of the real interpolation spaces. We determine the dual of (A0;A1)?;q;A when0![]()
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We investigate dual spaces of interpolation spaces defined by means of polygons. We first show that dual spaces may fail to be intermediate spaces with respect to the dual N-tuple, and then we prove that dual spaces of J-spaces can be identified[...]![]()
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For a compact metric space X let ? be a finite Borel measure on X. The authors investigate the asymptotic behavior of eigenvalues of integral operators on L2(X, ?). These integral operators are assumed to have a positive definite kernel which sa[...]![]()
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We determine the asymptotic order of decay of eigenvalues of weakly singular integral operators. The singularities are of quite general form, containing power and logarithmic terms. We give a unified elementary proof of all known results in this[...]![]()
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This paper deals with Besov spaces of logarithmic smoothness B-p,T(0,b) formed by periodic functions. We study embeddings of B-p,T(0,b) into Lorentz-Zygmund spaces L-p,L-q(log L)(beta). Our techniques rely on the approximation structure of B-p,T[...]![]()
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The paper deals with ideals of operators for which the sequence of their entropy numbers(en(T)) belongs to a Lorentz-Marcinkiewicz space `,q, where is a so-called function parameter. In the case (t) = tp the classical Lorentz space `p,q results[...]![]()
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We establish two-sided estimates for entropy numbers of embeddings between certain weighted Banach sequence spaces with mixed norms. These estimates are‘‘almost’’ sharp, in the sense that upper and lower bounds differ only by logarithmic terms a[...]![]()
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We consider limiting real interpolation spaces defined by using powers of iterated logarithms and show their description by means of the J -functional. Our results allow to complement some estimates on approximation of stochastic integrals.![]()
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We study spectral properties of operators on logarithmic perturbations of the real interpolation spaces with ? = 0 or 1. We also establish estimates for the measure of non-compactness of operators interpolated by those methods.![]()
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We provide a simple algorithm that constructs an exact minimizer for the E-functional E(t, f ; L?, BV) = inf ?g?L??t ? f ? g?BV . Here L?, BV stand for the space of bounded functions and the space of functions with bounded variation on the inter[...]![]()
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We establish abstract extrapolation results for entropy numbers of operators in Banach spaces. The results apply to extrapolation in the source spaces and also in the target spaces. As an illustration of the abstract results, applications to lim[...]![]()
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We establish compactness results for extrapolation constructions which correspond to the well-known Lions-Peetre compactness theorems of interpolation theory. Applications are given to compactness of certain limiting Sobolev embeddings.![]()
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The paper establishes estimates for ideal measures of operators interpolated by the real method in terms of the measures of their restrictions to a sequence of spaces modelled on the intersection. It also shows that the estimates are optimal.![]()
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We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space C-2. This answers a question posed by R. Grzaslewicz and K. John [7], who solved the corresponding problem for the real Hilbert space R-[...]![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. | Institute of Mathematics. Polish Academy of Sciences | 2008We review several results on interpolation of Banach algebras and factorization of weakly compact homomorphisms. We also establish a new result on interpolation of multilinear operators.![]()
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The paper deals with the entropy ideals generated by the Lorentz- Marcinkiewicz spaces of the type ? ? (?) where ? is a function parameter. The entropy ideal generated by ? ? (?) is the set of all operators between Banach spaces whose sequence o[...]![]()
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Fernández-Cabrera, Luz M. ; Cobos, Fernando ; Hernández, Francisco L. ; Sánchez, Víctor M. | Cambridge University Press | 2004We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.![]()
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Let (Y0, Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj ; (j = 0; 1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (?, q) such that the real interp[...]![]()
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We study the interpolation properties of compact bilinear operators by the general real method among quasi- Banach couples. As an application we show that commutators of Calderón-Zygmund bilinear operators S : Lp × Lq -? Lr are compact provided [...]![]()
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We show that the classical Lions-Peetre compactness theorems for Banach spaces (which are the main tools for proving all known compactness results in interpolation theory) fail in the locally convex case. We also prove a positive result assuming[...]![]()
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We investigate how compact operators behave under J and K interpolation methods for N spaces and two parameters. First we study those methods: relationship with those already existing in the literature, estimates for the norms of interpolated op[...]![]()
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Cobos, Fernando ; Fernández-Martínez, Pedro ; Martínez, Antón | Polish Acad Sciencies Inst Mathematics | 1999We investigate the behaviour of the measure of Iron-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.![]()
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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[...]![]()
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We develop a method suitable for interpolation of uniformly absolutely continuous operators. We then apply this method to establishing compactness of operators and embeddings especially in the limiting situations, where the classical interpolati[...]![]()
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Given an operator ideal J , the author describes the behaviour under interpolation of deviations of a linear operator T from the closed surjective hull of J and the closed injective hull of J . General results obtained in a collaboration with A.[...]![]()
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We investigate limiting J-interpolation methods for general Banach couples, not necessarily ordered. We also show their relationship with the interpolation methods defined by the unit square.![]()
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We study limiting K- and J-methods for arbitrary Banach couples. They are related by duality and they extend the methods already known in the ordered case. We investigate the behaviour of compact operators and we also discuss the representation [...]![]()
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Working with interpolation methods associated to polygons, a result of Cobos and Peetre guarantees that the interpolated operator is compact provided all but two restrictions of the operator (located in adjacent vertices) are compact. We charact[...]