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Complex Interpolation of Hardy‐Type Subspaces
Author(s) -
Kalton N. J.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951710114
Subject(s) - hardy space , mathematics , linear subspace , interpolation (computer graphics) , type (biology) , pure mathematics , interpolation space , function space , function (biology) , space (punctuation) , arc (geometry) , combinatorics , mathematical analysis , functional analysis , geometry , evolutionary biology , computer science , gene , biology , animation , ecology , biochemistry , chemistry , linguistics , computer graphics (images) , philosophy
We consider the problem of complex interpolation of certain Hardy‐type subspaces of Köthe function spaces. For example, suppose that X 0 and X 1 arc Köthe function spaces on the unit circle T. and let H X0 and H X1 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 X0 . H X1 ] 0 to coincide with H X0 where H X0 = [ H 0 . H 1 ] 0 . We develop a very general framework for such results and our methods apply to many more general situations including the vector–valued case.