Year: 1994
Type: preprint
Abstract: We consider the problem of complex interpolation of certain Hardy-type subspaces of Köthe function spaces. For example, suppose $X_0$ and $X_1$ are Köthe 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 $[H_{X_0},H_{X_1}]_θ$ to coincide with $H_{X_θ}$ where $X_θ=[X_0,X_1]_θ.$ We develop a very general framework for such results and our methods apply to many more general sitauations including the vector-valued case.
Source: arXiv (Cornell University)
Author: Kalton, Nigel J.
Institution: University of Missouri
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953058153