Interpolation between weighted Hardy spaces

Cwikel, Michael; McCarthy, John E.; Wolff, Thomas H.

doi:10.1090/S0002-9939-1992-1093595-4

Interpolation between weighted Hardy spaces
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by Michael Cwikel, John E. McCarthy and Thomas H. Wolff PDF

Proc. Amer. Math. Soc. 116 (1992), 381-388 Request permission

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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