Interpolation of bilinear operators between quasi-Banach spaces
The authors study interpolation, generated by the abstract method of means, of bilinear operators between quasi-Banach spaces. They introduce a notion of special type of convexity for bilinear operators between quasi-Banach couples and prove a bilinear interpolation theorem using the methods of means, under the condition that the associated convolution operator is bounded on the parameter spaces involved in the construction of these methods. The convexity parameters of the bilinear operators that take values in the so-called natural quasi-Banach spaces are nicely determined by the types of the domains of the quasi-Banach spaces. The authors then give applications of these results in the context of interpolation between quasi-Banach spaces generated by the real method of interpolation as well as to Calderón--Lozanovski spaces that include, in particular, Orlicz spaces. Finally, they discuss the abstract \(K\)- or \(J\)-interpolation method for bilinear operators between quasi-Banach spaces satisfying weaker convexity type conditions, in particular, bilinear interpolation theorems for Lorentz--Zygmund spaces.
scientific article; zbMATH DE number 5070790
scientific article