ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1（Rn） into L1（Rn） only if the function b is a constant [2]. In this article, we will discus...

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Bibliographic Details
Published inActa mathematica scientia Vol. 34; no. 2; pp. 387 - 393
Main Author 杨杰 王宇钊 陈文艺
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2014
Subjects
42B30
BMO
commutator
Hardy space
Hardy空间
LMO space
Pseudo-differential operator
伪微分算子
奇异积分算子
拟微分算子
换向器
有界性
端点估计
commutator
Pseudo-differential operator
42B30
Hardy space
LMO space
Online AccessGet full text
ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(14)60013-8

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Summary:It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb 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 Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc.
Bibliography:Jie YANG, Yuzhao WANG, Wenyi CHEN （School of Mathematics and Statistics, Wuhan University, Wuhan 330071, China）
42-1227/O
Hardy space; commutator; Pseudo-differential operator; LMO space
It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb 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 Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(14)60013-8