Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Endpoint estimates for certain commutators of fractional and singular integrals


Authors: Shanzhen Lu and Qiang Wu
Journal: Proc. Amer. Math. Soc. 131 (2003), 467-477
MSC (2000): Primary 42B20; Secondary 47B38, 47A30, 42B30, 42B35
DOI: https://doi.org/10.1090/S0002-9939-02-06548-6
Published electronically: May 17, 2002
MathSciNet review: 1933338
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B20, 47B38, 47A30, 42B30, 42B35

Retrieve articles in all journals with MSC (2000): 42B20, 47B38, 47A30, 42B30, 42B35


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: https://doi.org/10.1090/S0002-9939-02-06548-6
Keywords: Commutator, Hardy space, BMO, atom
Received by editor(s): May 2, 2001
Received by editor(s) in revised form: September 12, 2001
Published electronically: May 17, 2002
Additional Notes: This project was supported by the National 973 Foundation of China
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society