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Intermediate spaces and the complex method of interpolation for families of Banach spaces. (English) Zbl 0617.46078

This paper deals with the theory of complex interpolation for families of Banach spaces developed by R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher and G. Weiss. We identify the intermediate spaces of weighted \(L^ p\) spaces, \(L^ p\) spaces of Banach space valued functions, Lorentz spaces, \(\ell^ s_ p\) spaces of vector valued sequences, Sobolev and Besov- Lipschitz spaces.

MSC:

46M35 Abstract interpolation of topological vector spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A45 Sequence spaces (including Köthe sequence spaces)
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References:

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