VECTOR-VALUED HILBERT TRANSFORMS ALONG CURVES

被引：1
|
作者：
Hong, Guixiang [1 ,2 ]
Liu, Honghai [3 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[2] UCM, UC3M, Inst Ciencias Matemat, CSIC,UAM, C Nicolas Cabrera 13-15, Madrid 28049, Spain
[3] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454003, Henan, Peoples R China
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2016年 / 10卷 / 02期
基金：
中国国家自然科学基金; 欧洲研究理事会;
关键词：
Hilbert transforms along curves; weighted Hormander condition; UMD spaces; completely bounded; analytic interpolation; SINGULAR-INTEGRALS; FOURIER MULTIPLIERS;
D O I：
10.1215/17358787-3589397
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we show that Hilbert transforms along some curves are bounded on L-p (R-n; X) for some 1 < p < infinity 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 (R-n; X)-boundedness of anisotropic singular integrals by using the "method of rotations" of Calderon-Zygmund. All these results extend preexisting related ones.
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页码：430 / 450
页数：21
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