Sharp two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators

被引:7
作者
Bernardis, Ana L. [1 ]
Lorente, Maria [1 ]
机构
[1] Univ Malaga, Fac Ciencias, Dept Anal Matemat, E-29071 Malaga, Spain
关键词
weighted inequalities; Riemann-Liouville and Weyl fractional integrals; commutators;
D O I
10.1007/s00020-008-1600-y
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let b be a BMO function, 0 < alpha < 1 and I(alpha,b)(+,k) the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p,p) inequalities (p>1) and weighted endpoint estimates (p=1) for the operator I(alpha,b)(+,k) and for the pairs of weights of the type (w,Mw), where w is any weight and M is a suitable one-sided maximal operator. We also prove that, for A(infinity)(+) weights, the operator I(alpha,b)(+,k) is controlled in the Lp(w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide a different way to obtain known results about the operators I(alpha,b)(+,k). The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral I(alpha,b)(+,k).
引用
收藏
页码:449 / 475
页数:27
相关论文
共 27 条
[1]   WEIGHTED NORM INEQUALITIES FOR THE RIEMANN-LIOUVILLE AND WEYL FRACTIONAL INTEGRAL-OPERATORS [J].
ANDERSEN, KF ;
SAWYER, ET .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 308 (02) :547-558
[2]   Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type [J].
Bernardis, Ana ;
Hartzstein, Silvia ;
Pradolini, Gladis .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 322 (02) :825-846
[3]  
Carro MJ, 2005, INDIANA U MATH J, V54, P627
[4]   Extrapolation from A∞ weights and applications [J].
Cruz-Uribe, D ;
Martell, JM ;
Pérez, C .
JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 213 (02) :412-439
[5]  
de Rosa L, 2006, COMMENT MATH UNIV CA, V47, P35
[6]   WEIGHTED NORM INEQUALITIES FOR COMMUTATORS OF STRONGLY SINGULAR-INTEGRALS [J].
GARCIACUERVA, J ;
HARBOURE, E ;
SEGOVIA, C ;
TORREA, JL .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1991, 40 (04) :1397-1420
[7]  
Hewitt E, 1965, Real and Abstract Analysis
[8]  
Lorelli DR, 2002, J CARDIOVASC SURG, V43, P83
[9]   Weights for commutators of the one-sided discrete square function, the Weyl fractional integral and other one-sided operators [J].
Lorente, M ;
Riveros, MS .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2005, 135 :845-862
[10]   ONE-SIDED BMO SPACES [J].
MARTINREYES, FJ ;
DELATORRE, A .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1994, 49 :529-542