On commutators of fractional integrals

Authors:
Xuan Thinh Duong and Li Xin Yan

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3549-3557

MSC (2000):
Primary 42B20, 47B38

Published electronically:
July 14, 2004

MathSciNet review:
2084076

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . For a BMO function on , we show boundedness of the commutators from to , where . Our result of this boundedness still holds when is replaced by a Lipschitz domain of with infinite measure. We give applications to large classes of differential operators such as the magnetic Schrödinger operators and second-order elliptic operators of divergence form.

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Additional Information

**Xuan Thinh Duong**

Affiliation:
Department of Mathematics, Macquarie University, New South Wales 2109, Australia

Email:
duong@ics.mq.edu.au

**Li Xin Yan**

Affiliation:
Department of Mathematics, Zhongshan University, Guangzhou, 510275, People’s Republic of China

Address at time of publication:
Department of Mathematics, Macquarie University, New South Wales 2109, Australia

Email:
mcsylx@zsu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-04-07437-4

Keywords:
Gaussian bound,
fractional integrals,
{\rm BMO},
commutator

Received by editor(s):
January 3, 2003

Published electronically:
July 14, 2004

Additional Notes:
Both authors were supported by a grant from Australia Research Council, and the second author was also partially supported by the NNSF of China (Grant No. 10371134).

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2004
American Mathematical Society