Complex interpolation of Hardy-type subspaces

1994/02/11 by Kalton, Nigel J.
#46B #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9402206

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 \bold T, and let H_X0 and H_X1 be the corresponding Hardy spaces. Under mild conditions on X₀,X₁ we give a necessary and sufficient condition for the complex interpolation space [H_X0,H_X1]_θ to coincide with H_Xθ where X_θ=[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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