Complex interpolation of Hardy-type subspaces

Details Complex interpolation of Hardy-type subspaces Complex interpolation of Hardy-type subspaces

1994-02-11

arxiv.org/abs/math/9402206v1

Mathematics

Functional Analysis

Scientific paper

We consider the problem of complex interpolation of certain Hardy-type subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and $H_{X_1}$ be the corresponding Hardy spaces. Under mild conditions on $X_0,X_1$ we give a necessary and sufficient condition for the complex interpolation space $[H_{X_0},H_{X_1}]_{\theta}$ to coincide with $H_{X_{\theta}}$ where $X_{\theta}=[X_0,X_1]_{\theta}.$ We develop a very general framework for such results and our methods apply to many more general sitauations including the vector-valued case.

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