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Complex Interpolation of Normed and Quasinormed Spaces in Several Dimensions. II. Properties of Harmonic Interpolation
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
doi:10.2307/2001461
fatcat:xiqibio4j5a5nihcvecqdjvohi