带非光滑核的多线性Marcinkiewicz积分的加权界

王松柏

数学学报 ›› 2018, Vol. 61 ›› Issue (4) : 663-674.

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数学学报 ›› 2018, Vol. 61 ›› Issue (4) : 663-674. DOI: 10.12386/A2018sxxb0061
论文

带非光滑核的多线性Marcinkiewicz积分的加权界

    王松柏
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Weighted Bounds for Multilinear Marcinkiewicz Integrals with Nonsmooth Kernel

    Song Bai WANG
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摘要

我们引入了带非光滑核的多线性Marcinkiewicz积分算子.设p1,…,pm∈(1,∞)和p∈(0,+∞)满足1/p1+…+1/pm=1/p,记P=(p1,…,pm),又设向量权ω=(ω1,…,ωm)∈ APνω=∏k=1mωkp/pk,得到了Marcinkiewicz积分算子从Lp1ω1)×…×Lpmωm)到Lpνω)的常数界.

Abstract

We introduce the multilinear Marcinkiewicz integrals with nonsmooth kernel and get their the weighted bounds from Lp1(ω1)×…×Lpm(ωm) to Lp(νω) with p1, …, pm ∈ (1, ∞), 1/p1 + … + 1/pm=1/p and ω=(ω1, …, ωm) a multiple AP weights, where P=(p1, …, pm) and νω=∏k=1m ωkp/pk.

关键词

多线性Marcinkiewicz积分 / 非光滑核 / 多权

Key words

multilinear Marcinkiewicz integrals / non-smooth kernel / multiple weight

引用本文

导出引用
王松柏. 带非光滑核的多线性Marcinkiewicz积分的加权界. 数学学报, 2018, 61(4): 663-674 https://doi.org/10.12386/A2018sxxb0061
Song Bai WANG. Weighted Bounds for Multilinear Marcinkiewicz Integrals with Nonsmooth Kernel. Acta Mathematica Sinica, Chinese Series, 2018, 61(4): 663-674 https://doi.org/10.12386/A2018sxxb0061

参考文献

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基金

湖北省教育厅青年人才资助项目(Q20162504)

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