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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Interpolation of weighted and vector-valued Hardy spaces
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by Serguei V. Kisliakov and Quan Hua Xu PDF
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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 1-34
  • MSC: Primary 46E15; Secondary 42B30, 46E40, 46M35
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1236225-7
  • MathSciNet review: 1236225