Hardy space estimates for bi-parameter Littlewood-Paley square functions |
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Authors: | Fanghui LIAO Zhengyang LI |
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Institution: | 1. School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan 411105, China2. School of Mathematics and Computational Sciences, Hunan University of Science and Technology, Xiangtan 411201, China |
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Abstract: | Suppose that g(f) are bi-parameter Littlewood-Paley square functions which were introduced by H. Martikainen. It is known that the boundedness and the 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 to with p smaller than 1. |
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Keywords: | Hardy space Littlewood-Paley square function Journe's covering lemma atomic decomposition |
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