A note on UMD spaces and transference in vector-valued function spaces
1996 ◽
Vol 39
(3)
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pp. 485-490
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Keyword(s):
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.
2011 ◽
Vol 84
(1)
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pp. 44-48
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1987 ◽
Vol 101
(1)
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pp. 107-112
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Keyword(s):
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2014 ◽
Vol 21
(1)
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pp. 95-136
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Keyword(s):
2007 ◽
Vol 135
(09)
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pp. 2803-2810
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Keyword(s):
2012 ◽
Vol 389
(2)
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pp. 1173-1190
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