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Interpolation between weighted Hardy spaces

Authors: Michael Cwikel, John E. McCarthy and Thomas H. Wolff
Journal: Proc. Amer. Math. Soc. 116 (1992), 381-388
MSC: Primary 46E15; Secondary 30D55, 30H05, 46M35
MathSciNet review: 1093595
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Abstract: We prove that $ {H^p}(w_0^{1 - s}w_1^s)$ is an interpolation space of exponent $ s$ between $ {H^p}({w_0})$ and $ {H^p}({w_1})$ if and only if $ \log ({w_1}/{w_0})$ is in BMO. If $ \log ({w_1}/{w_0})$ fails to be in BMO, $ {H^p}(w_0^{1 - s}w_1^s)$ can still be an interpolation space, provided the range of $ w$ has sufficiently large gaps.

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Article copyright: © Copyright 1992 American Mathematical Society

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