Acta mathematica scientia, Series B >
ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS
Received date: 2012-06-09
Revised date: 2012-10-26
Online published: 2014-03-20
Supported by
The first author is supported by the National Science Foundation of China NSFC (11161044, 11131005).
It is well known that the commutator Tb of the Calder´on-Zygmund singular integral operator is bounded on Lp(Rn) for 1 < p < +∞ if and only if b ∈ 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 S01,δ with 0 ≤δ < 1, if b∈ LMO1, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L1(Rn) into BMO(Rn); If [b, Tσ ] is bounded from H1(Rn) into L1(Rn) or L1(Rn) into BMO(Rn), then, b ∈ LMOloc.
Key words： Hardy space; commutator; Pseudo-differential operator; LMO space
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 . DOI: 10.1016/S0252-9602(14)60013-8
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