On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMO

被引：24

作者：

Torres, Rodolfo H. ^{[1
,2
]}

Xue, Qingying ^{[3
]}

机构：

[1] Univ Kansas, Dept Math, 1460 Jayhawk Blvd, Lawrence, KS 66045 USA

[2] Univ Calif Riverside, Univ Off Bldg,Suite 200, Riverside, CA 92521 USA

[3] Beijing Normal Univ, Sch Math Sci, Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2020年 / 36卷 / 03期

关键词：

Calderon-Zygmund theory; singular integrals; commutators; bilinear operators; compact operators; bounded mean oscillation; CMO; VMO; HARDY SPACES; BOUNDEDNESS;

D O I：

10.4171/RMI/1156

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that the compactness of the commutators of point-wise multiplication with bilinear homogeneous Calderon-Zygmund operators acting on product of Lebesgue spaces is characterized by the multiplying function being in the space CMO. This space is the closure in BMO of its subspace of smooth functions with compact support. It is shown in this work that for bilinear Calderon-Zygmund operators arising from smooth (inhomogeneous) bilinear Fourier multipliers or bilinear pseudo-differential operators, one can actually consider multiplying functions in a new subspace of BMO larger than CMO.

引用

页码：939 / 956

页数：18

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