Author:
Asmar N. H.,Kelly B. P.,Montgomery-Smith S.
Abstract
A Banach space X is called an HT space if the Hilbert transform is bounded from Lp(X) into Lp(X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in Lp(X), 1 < p < ∞. Berkson, Gillespie and Muhly [5] showed that X ∈ HT ⇒ X ∈ ACF. In this note, we will show that X ∈ ACF ⇒ X ∈ UMD, thus providing a new proof of Bourgain's result X ∈ HT ⇒ X ∈ UMD.
Publisher
Cambridge University Press (CUP)
Reference14 articles.
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2. 13. Kelly B. P. , Distributional controlled representations acting on vector-valued functions spaces, Doctoral Dissertation, University of Missouri, 1994.
3. Transference Methods in Analysis
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