Complex Interpolation of Normed and Quasinormed Spaces in Several Dimensions. II. Properties of Harmonic Interpolation

Zbigniew Slodkowski
1990 Transactions of the American Mathematical Society  
This paper is a continuation of the study of harmonic interpolation families of normed or quasinormed spaces parametrized by points of a domain in C k . It is shown, among other things, that each of the following properties holds for all the intermediate quasinormed spaces, if it holds for all given boundary spaces: (I) being a normed space; (2) being a Hilbert space; (3) satisfying the triangle inequality by the rth power of the quasinorm; (4) being uniformly convex; and (5) being uniformly
more » ... being uniformly smooth. As a principal tool, the notion of a harmonic set valued function (a generalization of analytic multifunction) is introduced and studied.
doi:10.2307/2001461 fatcat:xiqibio4j5a5nihcvecqdjvohi