A Note on Umd Spaces and Transference in Vector-valued Function Spaces
نویسندگان
چکیده
Abstract. A Banach space X is called an HT space if the Hilbert transform is bounded from L(X) into L(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 L(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.
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