Θ-type Calderón-Zygmund operators with non-doubling measures

被引：0
作者：
Ru-long Xie
Li-sheng Shu
机构：
[1] University of Science and Technology of China,School of Mathematical Sciences
[2] Chaohu University,Department of Mathematics
[3] Anhui Normal University,Department of Mathematics
来源：
Acta Mathematicae Applicatae Sinica, English Series | 2013年 / 29卷
关键词：
non-doubling measure; -type Calderón-Zygmund operator, commutators; multilinear commutators; RBMO(µ) space; (µ) space; 42B20; 42B30;
D O I：
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中图分类号：
学科分类号：
摘要：
Let µ be a Radon measure on ℝd which may be non-doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Crn for all x∈ℝd, r > 0 and for some fixed 0 < n ≤ d. In this paper, under this assumption, we prove that θ-type Calderón-Zygmund operator which is bounded on L2(µ) is also bounded from L∞(µ) into RBMO(µ) and from Hatb1,∞ (µ) into L1(µ). According to the interpolation theorem introduced by Tolsa, the Lp(µ)-boundedness (1 < p < ∞) is established for θ-type Calderón-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type Calderón-Zygmund operator with RBMO(µ) function are bounded on Lp(µ) (1 < p < ∞).
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页码：263 / 280
页数：17
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