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arXiv · 1403.0177

Vector-valued Hilbert transforms along curves

Guixiang Hong·Honghai Liu
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Abstract

In this paper, we show that Hilbert transforms along some curves are bounded on $L^p({\mathbb R}^n;X)$ for some $1<p<\infty$ and some UMD spaces $X$. In particular, we prove that the Hilbert transform along some curves are completely $L^p$-bounded in the terminology from operator space theory. Moreover, we obtain the $L^p(\mathbb{R}^n;X)$-boundedness of anisotropic singular integrals by using the "method of rotations" of Calder\'{o}n-Zygmund. All these results extend the existing related ones.

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Guixiang Hong, Honghai Liu. 2014-03-02. Vector-valued Hilbert transforms along curves. https://doi.org/10.1215/17358787-3589397

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