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Endpoint estimates for certain commutators of fractional and singular integrals

Author(s): Shanzhen Lu; Qiang Wu
Journal: Proc. Amer. Math. Soc. 131 (2003), 467-477.
MSC (2000): Primary 42B20; Secondary 47B38, 47A30, 42B30, 42B35
Posted: May 17, 2002
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Abstract: In this paper, the authors obtain the endpoint estimates for a class of non-standard commutators with higher order remainders and their variants. Moreover, the authors show that these operators are actually not bounded in certain cases.

References:

[1]
B. Bajsanski and R. Coifman, On singular integrals, Proc. Sympos. Pure Math. Vol 10, Amer. Math. Soc. Providence, R. I. (1967), 1-17. MR 38:6405

[2]
A. P. Calderón, On algebras of singular integral operators, Proc. Sympos. Pure Math. Vol 10, Amer. Math. Soc. Providence, R. I. (1967), 18-55. MR 52:15112

[3]
W. Chen and G. Hu, Weak type ( $H^1,\, L^1$) estimate for a multilinear singular integral operator, Adv. in Math., 30:1 (2001), 63-69. CMP 2001:12

[4]
J. Cohen and J. Gosselin, A BMO estimate for multilinear singular integrals, Illinois J. Math. 30 (1986), 445-464. MR 87k:42022

[5]
E. Harboure, C. Segovia and J. L. Torrea, Boundedness of commutators of fractional and singular integrals for the extreme values of $p$, Illinois J. Math. 41 (1997), 676-700. MR 99j:42025

[6]
S. Hofmann, On certain non-standard Calderón-Zygmund operators, Studia Math. 109 (1994), 105-131. MR 95h:42021

[7]
G. Hu and D. Yang, Multilinear oscillatory singular integral operators on Hardy spaces, Chinese J. of Contemporary Math. 18 (1997), 403-413. MR 99g:42017

[8]
E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, N. J., 1993. MR 95c:42002

[9]
Q. Wu and D. Yang, On fractional multilinear singular integrals, Math. Nachr. to appear.

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Additional Information:

Shanzhen Lu
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China
Email: lusz@bnu.edu.cn

Qiang Wu
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China

DOI: 10.1090/S0002-9939-02-06548-6
PII: S 0002-9939(02)06548-6
Keywords: Commutator, Hardy space, BMO, atom
Received by editor(s): May 2, 2001
Received by editor(s) in revised form: September 12, 2001
Posted: May 17, 2002
Additional Notes: This project was supported by the National 973 Foundation of China
Communicated by: Andreas Seeger
Copyright of article: Copyright 2002, American Mathematical Society

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