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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[...]