Browse > Article
http://dx.doi.org/10.4134/CKMS.2008.23.1.049

SHARP ESTIMATES FOR MULTILINEAR COMMUTATOR OF LITTLEWOOD-PALEY OPERATOR  

Hao, Jinliang (DEPARTMENT OF MATHEMATICS CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY)
Liu, Lanzhe (DEPARTMENT OF MATHEMATICS CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.1, 2008 , pp. 49-59 More about this Journal
Abstract
In this paper, we prove the sharp estimates for multilinear commutator related to Littlewood-Paley operator. By using the sharp estimates, we obtained the weighted $L^p$-norm inequality for the multilinear commutator for 1 < p < $\infty$.
Keywords
multilinear commutator; Littlewood-Paley operator; BMO; sharp inequality;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635   DOI
2 J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. 16, Amsterdam, 1985
3 J. Alvarez, R. J. Babgy, D. S. Kurtz, and C. Perez, Weighted estimates for commutators of linear operators, Studia Math. 104 (1993), 195-209   DOI
4 R. Coifman and Y. Meyer, Wavelets, Calderon-Zygmund and Multilinear Operators, Cambridge Studies in Advanced Math. 48, Cambridge University Press, Cambridge, 1997
5 L. Z. Liu, Weighted weak type estimates for commutators of Littlewood-Paley operator, Japanese J. Math. 29 (2003), no. 1, 1-13   DOI
6 L. Z. Liu, The continuity of commutators on Triebel-Lizorkin spaces, Integral Equations and Operator Theory 49 (2004), no. 1, 65-76   DOI
7 C. Perez, Endpoint estimate for commutators of singular integral operators, J. Func. Anal. 128 (1995), 163-185   DOI   ScienceOn
8 C. Perez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J. 49 (2001), 23-37   DOI
9 A. Torchinsky, The Real Variable Methods in Harmonic Analysis, Pure and Applied Math. 123, Academic Press, New York, 1986
10 C. Perez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators, J. London Math. Soc. 65 (2002), 672-692   DOI
11 G. Hu and D. C. Yang, A variant sharp estimate for multilinear singular integral operators, Studia Math. 141 (2000), 25-42
12 E. M. Stein, Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993