The boundedness of Marcinkiewicz integral with variable kernel

Chin Cheng Lin, Ying Chieh Lin, Xiangxing Tao, Xiao Yu

研究成果: 雜誌貢獻期刊論文同行評審

4 引文 斯高帕斯(Scopus)

摘要

In this article, we study the fractional Marcinkiewicz integral with variable kernel defined by where 0 < α ≤ 2. We first prove that μΩ,α is bounded from L2n/n+α(Rn) to L2(Rn) without any smoothness assumption on the kernel Ω. Then we show that, if the kernel Ω satisfies a class of Dini condition, μΩ,α is bounded from Hp(Rn) (p ≤ 1) to Hq(Rn), where 1/q = 1/p - α/2n. As corollary of the above results, we obtain the Lp - Lq (1 < p < 2) boundedness of this fractional Marcinkiewicz integral.

原文???core.languages.en_GB???
頁(從 - 到)197-217
頁數21
期刊Illinois Journal of Mathematics
53
發行號1
DOIs
出版狀態已出版 - 2009

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