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Báo cáo hóa học: " Estimates for the multiple singular integrals via extrapolation"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Estimates for the multiple singular integrals via extrapolation | Journal of Inequalities and Applications SpringerOpen0 This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text HTML versions will be made available soon. Estimates for the multiple singular integrals via extrapolation Journal of Inequalities and Applications 2011 2011 115 doi 10.1186 1029-242X-2011-115 Meng Qu qumeng@mail.ahnu.edu.cn ISSN 1029-242X Article type Research Submission date 9 July 2011 Acceptance date 21 November 2011 Publication date 21 November 2011 Article URL http www.journalofinequalitiesandapplications.com content 2011 1 This peer-reviewed article was published immediately upon acceptance. It can be downloaded printed and distributed freely for any purposes see copyright notice below . For information about publishing your research in Journal of Inequalities and Applications go to http www.journalofinequalitiesandapplications.com authors instructions For information about other SpringerOpen publications go to http www.springeropen.com 2011 Qu licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Estimates for the multiple singular integrals via extrapolation Meng Qu School of Mathematical and Computer Sciences Anhui Normal University Wuhu 241002 People s Republic of China Corresponding author qumeng@mail.ahnu.edu.cn Abstract This paper is devoted to the study on the Lp estimates for the multiple singular integrals with rough kernels on product spaces Rn X Rm n m 2 . By means of extrapolation method and Fourier transform estimate we prove that the multiple singular integral operators are bounded on Lp Rn X Rm for the kernel functions 2 L log L 2 Sn 1 X Sm 1 h 2 Aa R X R a 2 1 2 . Furthermore we prove that when 2 L log L 2 S 1 X S 1 and h satisfying a log type .