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April 2016 Vector-valued Hilbert transforms along curves
Guixiang Hong, Honghai Liu
Banach J. Math. Anal. 10(2): 430-450 (April 2016). DOI: 10.1215/17358787-3589397

Abstract

In this paper, we show that Hilbert transforms along some curves are bounded on Lp(Rn;X) for some 1<p< and some UMD spaces X. In particular, we prove that Hilbert transforms along some curves are completely Lp-bounded in the terminology from operator space theory. Moreover, we obtain the Lp(Rn;X)-boundedness of anisotropic singular integrals by using the “method of rotations” of Calderón–Zygmund. All these results extend preexisting related ones.

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Guixiang Hong. Honghai Liu. "Vector-valued Hilbert transforms along curves." Banach J. Math. Anal. 10 (2) 430 - 450, April 2016. https://doi.org/10.1215/17358787-3589397

Information

Received: 9 April 2015; Accepted: 27 July 2015; Published: April 2016
First available in Project Euclid: 19 April 2016

zbMATH: 1337.43003
MathSciNet: MR3489648
Digital Object Identifier: 10.1215/17358787-3589397

Subjects:
Primary: ‎43A32
Secondary: 46B99

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 2 • April 2016
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