Complex interpolation of Hardy-type subspaces
Nigel J. Kalton
Abstract
We consider the problem of complex interpolation of certain Hardy-type subspaces of Köthe function spaces. For example, suppose X0 and X1 are Köthe function spaces on the unit circle T, and let HX0 and HX1 be the corresponding Hardy spaces. Under mild conditions on X0,X1 we give a necessary and sufficient condition for the complex interpolation space [HX0,HX1]θ to coincide with HXθ where Xθ=[X0,X1]θ. 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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