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Báo cáo hóa học: " Research Article A Class of Commutators for Multilinear Fractional Integrals in Nonhomogeneous Spaces"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Class of Commutators for Multilinear Fractional Integrals in Nonhomogeneous Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 373050 17 pages doi 10.1155 2008 373050 Research Article A Class of Commutators for Multilinear Fractional Integrals in Nonhomogeneous Spaces Jiali Lian and Huoxiong Wu School of Mathematical Sciences Xiamen University Xiamen Fujian 361005 China Correspondence should be addressed to Huoxiong Wu huoxwu@xmu.edu.cn Received 3 March 2008 Accepted 16 July 2008 Recommended by Nikolaos Papageorgiou Let y be a nondoubling measure on Rd .A class of commutators associated with multilinear fractional integrals and RBMO y functions are introduced and shown to be bounded on product of Lebesgue spaces with y. Copyright 2008 J. Lian and H. Wu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In recent years the study of multilinear operators and their commutator has been attracting many researchers. Many results which parallel to the linear theory of classical integral operators are obtained. For details one can see 1-4 and so forth. Meanwhile as a further development harmonic analysis on Rd with nondoubling measures has been developed rapidly. Many results of singular integrals and the related operators on Euclidean spaces with Lebesgue measure have been generalized to the Lebesgue spaces with nondoubling measures see 5-10 etc. . Motivated by 5 8 we will consider the commutators generated by a class of multilinear fractional integrals and RBMO functions with nondoubling measure which were introduced by Tolsa in 11 . Before stating our results we recall some definitions and notations. Let y be a Radon measure on Rd satisfying the following growth condition there exist constants C 0 and n e 0 d such that yQ ci Q n 1.1 for any cube Q c Rd with sides parallel to the coordinate axes where l Q stands for the side .