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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 Boundedness of Parametrized Littlewood-Paley Operators with Nondoubling Measures | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 141379 25 pages doi 10.1155 2008 141379 Research Article Boundedness of Parametrized Littlewood-Paley Operators with Nondoubling Measures Haibo Lin1 and Yan Meng2 1 School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China 2 School of Information Renmin University of China Beijing 100872 China Correspondence should be addressed to Yan Meng mengyan@ruc.edu.cn Received 2 April 2008 Accepted 30 July 2008 Recommended by Siegfried Carl Let y be a nonnegative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that y B x r Crn for all x e Rd r 0 and some fixed n e 0 d . In this paper the authors prove that for suitable indexes p and X- the parametrized g function JCP is bounded on Ư y for p e 2 to with the assumption that the kernel of the operator jCy satisfies some Hormander-type condition and is bounded from L1 y into weak L1 y with the assumption that the kernel satisfies certain slightly stronger Hormander-type condition. As a corollary Jt f with the kernel satisfying the above stronger Hormander-type condition is bounded on ư y for p e 1 2 . Moreover the authors prove that for suitable indexes p and A JCP is bounded from Lto y into RBLO y the space of regular bounded lower oscillation functions if the kernel satisfies the Hormander-type condition and from the Hardy space H 1 y into L1 y if the kernel satisfies the above stronger Hormander-type condition. The corresponding properties for the parametrized area integral MPS are also established in this paper. Copyright 2008 H. Lin and Y. Meng. 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 Let y .
