Frontiers of Mathematics in China >
Weighted estimates for commutators of one-sided oscillatory integral operators
Received date: 27 Dec 2010
Accepted date: 19 Feb 2011
Published date: 01 Jun 2011
Copyright
In this paper, we study the weighted norm inequalities for commutators formed by a class of one-sided oscillatory integral operators and functions in one-sided BMO spaces.
Key words: Commutator; one-sided oscillatory integral; BMO; one-sided weight
Shaoguang SHI , Zunwei FU , Shanzhen LU . Weighted estimates for commutators of one-sided oscillatory integral operators[J]. Frontiers of Mathematics in China, 2011 , 6(3) : 507 -516 . DOI: 10.1007/s11464-011-0113-1
1 |
Acrarez J, Bagby R J, Kurtz D S, Perez C. Weighted estimates for commutators of linear operators. Studia Math, 1993, 104(2): 195-209
|
2 |
Aimar H, Forzani L, Martín-Reyes F J. On weighted inequalities for one-sided singular integrals. Proc Amer Math Soc, 1997, 125: 2057-2064
|
3 |
Chanillo S, Christ M. Weak (1,1) bounds for oscillatory integrals. Duke Math J, 1987, 55: 141-155
|
4 |
Coifman R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces in several variables. Ann Math, 1976, 103: 611-635
|
5 |
Ding Y, Lu S Z. Weighted Lp-boundedness for higher order commutators of oscillatory singular integrals. Tohoku Math J, 1996, 48: 437-449
|
6 |
Fu Z W, Shi S G, Lu S Z. Weighted norm inequality for the one-sided oscillatory singular operators. Preprint
|
7 |
Lorente M, Riveros M S. Weighted inequlities for commutators of one-sided singular integrals. Comment Math Univ Carolinae, 2002, 43(1): 83-101
|
8 |
Lu S Z, Wu H X. Oscillatory singular integrals and commutators with rough kernels. Ann Sci Math Quebec, 2003, 27: 47-66
|
9 |
Lu S Z, Zhang Y. Weighted norm inequality of a class of oscillatory singular operators. Chin Sci Bull, 1992, 37: 9-13
|
10 |
Martín-Reyes F J, Pirk L, Torre A be la.
|
11 |
Martín-Reyes F J, Torre A be la. One-sided BMO spaces. J London Math Soc, 1994, 49: 529-542
|
12 |
Ricci F, Stein E M. Harmonic analysis on nilpotant groups and singular integrals I: Oscillatory integrals. J Funct Anal, 1987, 73: 179-194
|
13 |
Riveros M S, Cordoda , Torre A D. On the best ranges for
|
14 |
Sato S. Weighted weak type (1,1) estimates for oscillatory integrals. Studia Math, 2001, 47: 1-17
|
15 |
Sawyer E. Weighted inequalities for the one-sided Hardy-Littlewood maximal function. Trans Amer Math Soc, 1986, 297: 53-61
|
16 |
Stein E M, Weiss G. Interpolation of operators with change of measures. Trans Amer Math Soc, 1958, 87: 159-172
|
17 |
Wu H X. Boundedness of higher order commutators of oscillatory singular integrals with rough kernels. Studia Math, 2005, 167(1): 29-43
|
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