Complex interpolation functors with a family of quasi-power function parameters. (English) Zbl 0805.46075

Summary: For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskij construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters which are quasi-powers with a logarithmic factor.


46M35 Abstract interpolation of topological vector spaces
46B70 Interpolation between normed linear spaces
46M15 Categories, functors in functional analysis
46B03 Isomorphic theory (including renorming) of Banach spaces
Full Text: DOI EuDML