Hardy space estimates for bi-parameter Littlewood-Paley square functions  

作　　者：Fanghui LIAO Zhengyang LI 

机构地区：[1]School of Mathematics and Computational Sciences,Xiangtan University,Xiangtan 411105,China [2]School of Mathematics and Computational Sciences,Hunan University of Science and Technology,Xiangtan 411201,China

出　　处：《Frontiers of Mathematics in China》2020年第2期333-349,共17页中国高等学校学术文摘·数学（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.11901495,11771345);the Hunan Provincial Natural Science Foundation(2019JJ50573);the Hunan Education Department Project(18C0109).

摘　　要：Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)have been proved by H.Martikainen and by Z.Li and Q.Xue,respectively.In this paper,we apply the vector-valued theory,the atomic decomposition of product Hardy spaces,and Journe’s covering lemma to show that g(f)are bounded from H^p(R^n×R^m)to Lp(R^n×R^m)with p smaller than 1.

关 键 词：Hardy space Littlewood-Paley square function Journe’s covering lemma atomic decomposition 

分 类 号：O17[理学—数学]