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Endpoint estimates for the commutator of pseudo-differential operators

Authors
  • YANG, Jie
  • WANG, Yuzhao
  • CHEN, Wenyi1
  • 1 School of Mathematics and Statistics
Type
Published Article
Journal
Acta Mathematica Scientia
Publication Date
Jan 01, 2014
Volume
34
Issue
2
Pages
387–393
Identifiers
DOI: 10.1016/S0252-9602(14)60013-8
Source
Elsevier
Keywords
License
Unknown

Abstract

It is well known that the commutator Tb of the Calderón-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 ∈ LMO∞, 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.

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