Vector-valued Hilbert transforms along curves

Guixiang Hong; Honghai Liu

doi:10.1215/17358787-3589397

Vector-valued Hilbert transforms along curves

Guixiang Hong
, Honghai Liu^*

^*Corresponding author for this work

Wuhan University
CSIC-UAM-UC3M-UCM - Instituto de Ciencias Matematicas (ICMAT)
Henan Polytechnic University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	430-450
Number of pages	21
Journal	Banach Journal of Mathematical Analysis
Volume	10
Issue number	2
DOIs	https://doi.org/10.1215/17358787-3589397
State	Published - 1 Apr 2016
Externally published	Yes

Keywords

Analytic interpolation
Completely bounded
Hilbert transforms along curves
UMD spaces
Weighted Hörmander condition

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10.1215/17358787-3589397

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title = "Vector-valued Hilbert transforms along curves",

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 Calder{\'o}n-Zygmund. All these results extend preexisting related ones.",

keywords = "Analytic interpolation, Completely bounded, Hilbert transforms along curves, UMD spaces, Weighted H{\"o}rmander condition",

author = "Guixiang Hong and Honghai Liu",

note = "Publisher Copyright: {\textcopyright} 2016 by the Tusi Mathematical Research Group.",

year = "2016",

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doi = "10.1215/17358787-3589397",

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AU - Liu, Honghai

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AB - 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.

KW - Analytic interpolation

KW - Completely bounded

KW - Hilbert transforms along curves

KW - UMD spaces

KW - Weighted Hörmander condition

UR - https://www.scopus.com/pages/publications/85046366332

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DO - 10.1215/17358787-3589397

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VL - 10

SP - 430

EP - 450

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

IS - 2

ER -

Vector-valued Hilbert transforms along curves

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Keywords

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