一类新型BMO空间

王定怀, 周疆

数学学报 ›› 2017, Vol. 60 ›› Issue (5) : 833-846.

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数学学报 ›› 2017, Vol. 60 ›› Issue (5) : 833-846. DOI: 10.12386/A2017sxxb0071
论文

一类新型BMO空间

    王定怀, 周疆
作者信息 +

Some New Classes of BMO Spaces

    Ding Huai WANG, Jiang ZHOU
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文章历史 +

摘要

引进了弱型有界平均震荡函数空间WBMOq,1 < q < ∞,它是类似于弱型勒贝格空间Lq,∞所对应的 BMO空间. 证明了||·||*(BMO 范数)与||·||WBMOq之间的等价特征刻画. 作为应用,对于p∈(1,∞)和1/q=1/p-α/n,交换子[b,Iα] 是从LpLq,∞的有界算子,当且仅当局部可积函数b属于BMO空间,其中Iα表示分数次积分算子. 另外,还引进以及学习了弱型的中心有界平均震荡空间Wq.

Abstract

We introduce the weak bounded mean oscillation spaces WBMOq, 1 < q < ∞, which are the analog of weak Lebesgue spaces Lq,∞ in the setting of BMO space. It is obtained that the equivalence between the norms||·||* (the BMO norm) and||·||WBMOq. As an application, we show that the commutator[b,Iα] is bounded from Lp to Lq,∞ for some p∈(1,∞) and 1/q=1/p-α/n, if and only if b∈ BMO, where Iα is a fractional integral operator. Also, we introduce and study the weak central bounded mean oscillation spaces Wq.

关键词

BMO空间 / 交换子 / 等价性 / 分数次积分算子 / 弱型勒贝格空间

Key words

BMO space / commutator / equivalence / fractional integral / weak Lebesgue space

引用本文

导出引用
王定怀, 周疆. 一类新型BMO空间. 数学学报, 2017, 60(5): 833-846 https://doi.org/10.12386/A2017sxxb0071
Ding Huai WANG, Jiang ZHOU. Some New Classes of BMO Spaces. Acta Mathematica Sinica, Chinese Series, 2017, 60(5): 833-846 https://doi.org/10.12386/A2017sxxb0071

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基金

国家自然科学基金资助项目(11661075

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