Interpolation of weighted and vector-valued Hardy spaces

Kisliakov, Serguei V.; Xu, Quan Hua

doi:10.1090/S0002-9947-1994-1236225-7

Interpolation of weighted and vector-valued Hardy spaces
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Trans. Amer. Math. Soc. 343 (1994), 1-34 Request permission

Abstract:

Real and complex interpolation methods, when applied to the couple $({H^{{p_0}}}({E_0};{w_0}),{H^{{p_1}}}({E_1};{w_1}))$, give what is expected if ${E_0}$ and ${E_1}$ are quasi-Banach lattices of measurable functions satisfying certain mild conditions and if $\log (w_0^{1/{p_0}}w_1^{ - 1/{p_1}}) \in {\text {BMO}} ({w_0},{w_1}$ being weights on the unit circle). The last condition is in fact necessary. (It is expected, of course, that the resulting spaces coincide with the subspaces of analytic functions in the corresponding interpolation spaces for the couple $({L^{{p_0}}}({E_0};{w_0}),{L^{{p_1}}}({E_1};{w_1})).)$

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