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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[...]texto impreso
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 ?.texto impreso
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[...]texto impreso
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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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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 [...]texto impreso
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[...]texto impreso
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[...]texto impreso
We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.texto impreso
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[...]texto impreso
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.texto impreso
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.texto impreso
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 [...]
