ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

doi:10.1016/S0252-9602(14)60013-8

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (2): 387-393.doi: 10.1016/S0252-9602(14)60013-8

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

杨杰|王宇钊|陈文艺

School of Mathematics and Statistics, Wuhan University, Wuhan 430071, China

收稿日期:2012-06-09 修回日期:2012-10-26 出版日期:2014-03-20 发布日期:2014-03-20
基金资助:
The first author is supported by the National Science Foundation of China NSFC (11161044, 11131005).

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

YANG Jie, WANG Yu-Zhao, CHEN Wen-Yi

School of Mathematics and Statistics, Wuhan University, Wuhan 430071, China

Received:2012-06-09 Revised:2012-10-26 Online:2014-03-20 Published:2014-03-20
Supported by:
The first author is supported by the National Science Foundation of China NSFC (11161044, 11131005).

摘要/Abstract

摘要：

It is well known that the commutator T_bof the Calder´on-Zygmund singular integral operator is bounded on L^p(Rⁿ) for 1 < p < +∞ if and only if b ∈ BMO [1]. On the other hand, the commutator T_b is bounded from H¹(Rⁿ) into L¹(Rⁿ) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H¹. Let T^σ be the operators that its symbol is S⁰_1,δ with 0 ≤δ < 1, if b∈ LMO1, then, the commutator [b, T^σ] is bounded from H¹(Rⁿ) into L¹(Rⁿ) and from L¹(Rⁿ) into BMO(Rⁿ); If [b, T^σ ] is bounded from H¹(Rⁿ) into L¹(Rⁿ) or L¹(Rⁿ) into BMO(Rⁿ), then, b ∈ LMOloc.

关键词: Hardy space, commutator, Pseudo-differential operator, LMO space

Abstract:

Key words: Hardy space, commutator, Pseudo-differential operator, LMO space

中图分类号:

42B30

杨杰, 王宇钊, 陈文艺. ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS[J]. 数学物理学报(英文版), 2014, 34(2): 387-393.

YANG Jie, WANG Yu-Zhao, CHEN Wen-Yi. ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS[J]. Acta mathematica scientia,Series B, 2014, 34(2): 387-393.

参考文献

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ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

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