Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture

被引:51
作者
Cruz-Uribe, D.
Martell, J. M.
Perez, C. [1 ]
机构
[1] Univ Seville, Fac Matemat, Dept Analisis Matemat, Seville 41080, Spain
[2] Trinity Coll, Dept Math, Hartford, CT 06106 USA
[3] CSIC, Inst Matemat & Fis Fundamental, E-28006 Madrid, Spain
关键词
weights; Hilbert transform; singular integral operators; sarason conjecture; toeplitz operator; maximal functions; commutators;
D O I
10.1016/j.aim.2007.05.022
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove two-weight norm inequalities for Calderon-Zygmund singular integrals that are sharp for the Hilbert transform and for the Riesz transforms. In addition, we give results for the dyadic square function and for commutators of singular integrals. As an application we give new results for the Sarason conjecture on the product of unbounded Toeplitz operators on Hardy spaces. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码:647 / 676
页数:30
相关论文
共 56 条
[1]  
ALVAREZ J, 1994, B UNIONE MAT ITAL, V8A, P123
[2]  
[Anonymous], 1959, TRIGONOMETRIC SERIES
[3]   SOME WEIGHTED NORM INEQUALITIES CONCERNING THE SCHRODINGER-OPERATORS [J].
CHANG, SYA ;
WILSON, JM ;
WOLFF, TH .
COMMENTARII MATHEMATICI HELVETICI, 1985, 60 (02) :217-246
[4]  
COIFMAN RR, 1974, STUD MATH, V51, P241
[5]  
Cotlar M., 1983, WADSWORTH MATH SER, VII, P306
[6]  
COTLAR M, 1979, P S PURE MATH 1, V35, P383
[7]   Extrapolation from A∞ weights and applications [J].
Cruz-Uribe, D ;
Martell, JM ;
Pérez, C .
JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 213 (02) :412-439
[8]  
Cruz-Uribe D, 2002, HOUSTON J MATH, V28, P169
[9]   Two weight extrapolation via the maximal operator [J].
Cruz-Uribe, D ;
Pérez, C .
JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 174 (01) :1-17
[10]  
Cruz-Uribe D, 1999, MATH RES LETT, V6, P417