SHARP ESTIMATES FOR MULTILINEAR COMMUTATOR OF LITTLEWOOD-PALEY OPERATOR

Title & Authors
SHARP ESTIMATES FOR MULTILINEAR COMMUTATOR OF LITTLEWOOD-PALEY OPERATOR
Hao, Jinliang; Liu, Lanzhe;

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 $\small{L^p}$-norm inequality for the multilinear commutator for 1 < p < $\small{\infty}$.
Keywords
multilinear commutator;Littlewood-Paley operator;BMO;sharp inequality;
Language
English
Cited by
References
1.
J. Alvarez, R. J. Babgy, D. S. Kurtz, and C. Perez, Weighted estimates for commutators of linear operators, Studia Math. 104 (1993), 195-209

2.
R. Coifman and Y. Meyer, Wavelets, Calderon-Zygmund and Multilinear Operators, Cambridge Studies in Advanced Math. 48, Cambridge University Press, Cambridge, 1997

3.
R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635

4.
J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. 16, Amsterdam, 1985

5.
G. Hu and D. C. Yang, A variant sharp estimate for multilinear singular integral operators, Studia Math. 141 (2000), 25-42

6.
L. Z. Liu, Weighted weak type estimates for commutators of Littlewood-Paley operator, Japanese J. Math. 29 (2003), no. 1, 1-13

7.
L. Z. Liu, The continuity of commutators on Triebel-Lizorkin spaces, Integral Equations and Operator Theory 49 (2004), no. 1, 65-76

8.
C. Perez, Endpoint estimate for commutators of singular integral operators, J. Func. Anal. 128 (1995), 163-185

9.
C. Perez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J. 49 (2001), 23-37

10.
C. Perez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators, J. London Math. Soc. 65 (2002), 672-692

11.
E. M. Stein, Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993

12.
A. Torchinsky, The Real Variable Methods in Harmonic Analysis, Pure and Applied Math. 123, Academic Press, New York, 1986