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Journal of Function Spaces
Volume 2016, Article ID 4876146, 11 pages
Research Article

Multilinear Square Functions with Kernels of Dini’s Type

1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
2School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received 9 December 2015; Accepted 31 January 2016

Academic Editor: Rodolfo H. Torres

Copyright © 2016 Zengyan Si and Qingying Xue. 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.


Let be a multilinear square function with a kernel satisfying Dini(1) condition and let be the corresponding multilinear maximal square function. In this paper, first, we showed that is bounded from to Secondly, we obtained that if each , then and are bounded from to and if there is , then and are bounded from to , where Furthermore, we established the weighted strong and weak type boundedness for and on weighted Morrey type spaces, respectively.