Real Interpolation of Compact Bilinear Operators

Interpolation of compact bilinear operators among quasi‐Banach spaces and applications

“…Section 4 contains the abstract results on interpolation of compact bilinear operators in the setting of the quasi-Banach spaces. The results extend those of Fernández-Cabrera and Martínez [23,24] for the Banach case. We omit details when the arguments of [23,24] need only minor modifications, but sometimes we must give separate proofs.…”

“…The results extend those of Fernández-Cabrera and Martínez [23,24] for the Banach case. We omit details when the arguments of [23,24] need only minor modifications, but sometimes we must give separate proofs. Applications of these abstract results are given in the last two sections.…”

“…For the Banach case, that is, when are Banach couples, and are Banach sequence lattices satisfying , and , then Theorem recovers [, Theorem 3.1]. In particular, in the Banach case Theorem improves [, Theorem 5.8].…”

“…They satisfy the corresponding versions of (i), (ii) and (iii). Next we split the operator as in the Banach case [, Theorem 3.1] and we work with each piece with the help of results of Section 3 and Theorems and . Using (ii), for we obtain .…”

“…Results of refer to the general real method which is defined by replacing the weighted norm used in by a more general lattice norm. The outcome is a very flexible method.…”