Sharp Two Weight Inequalities for Commutators of Riemann-Liouville and Weyl Fractional Integral Operators |
| |
Authors: | Ana L Bernardis María Lorente |
| |
Institution: | (1) IMAL-CONICET, Güemes 3450, 3000 Santa Fe, Argentina;(2) Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain |
| |
Abstract: | Let b be a BMO function, and 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 and for the pairs of weights of the type (w, ), where w is any weight and is a suitable one-sided maximal operator. We also prove that, for weights, the operator is controlled in the L
p
(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 . The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral
This research has been partially supported by Spanish goverment Grant MTM2005-8350-C03-02. The first author was also supported
by CONICET, ANPCyT and CAI+D-UNL. The second author was also supported by Junta de Andalucía Grant FQM 354. |
| |
Keywords: | " target="_blank"> Weighted inequalities Riemann-Liouville and Weyl fractional integrals commutators |
本文献已被 SpringerLink 等数据库收录! |
|