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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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Hardy spaces of vector-valued functions: duality
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by Oscar Blasco PDF
Trans. Amer. Math. Soc. 308 (1988), 495-507 Request permission

Abstract:

We prove here that the Hardy space of $B$-valued functions ${H^1}(B)$ defined by using the conjugate function and the one defined in terms of $B$-valued atoms do not coincide for a general Banach space. The condition for them to coincide is the UMD property on $B$. We also characterize the dual space of both spaces, the first one by using ${B^{\ast }}$-valued distributions and the second one in terms of a new space of vector-valued measures, denoted $\mathcal {B}\mathcal {M}\mathcal {O}({B^{\ast }})$, which coincides with the classical $\operatorname {BMO} ({B^{\ast }})$ of functions when ${B^{\ast }}$ has the RNP.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 308 (1988), 495-507
  • MSC: Primary 46E40; Secondary 28B05, 42B30, 46E30
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0951618-8
  • MathSciNet review: 951618