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arXiv 0903.3780math.CAmath.FA
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用局部分数次积分的交换子刻画与高斯测度相关的BMO

Characterizations of BMO Associated with Gauss Measures via Commutators of Local Fractional Integrals

Liguang Liu, Dachun Yang

备注：
25 pages; Israel J. Math. (to appear)
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摘要：

令所有$x\in{\mathbb R}^n$的$dγ(x)\equivπ^{-n/2}e^{-|x|^2}dx$为${\mathbb R}^n$上的高斯测度。本文利用局部分数次积分算子或局部分数次极大算子的扩张子建立了Mauceri和Meda的BMO $(γ)$空间的特征。为此，首先证明了这样一个$β$阶局部分数次积分算子从$L^p(γ)$到$L^{p/(1-pβ)}(γ)$，或从Mauceri和Meda的Hardy空间$H^1(γ)$到$L^{1/(1-β)}(γ)$，或从$L^{1/β}(γ)$到BMO $(γ)$是有界的，其中$β\in(0, 1)$和$p\in(1, 1/β)$ .

英文摘要：

Let $dγ(x)\equivπ^{-n/2}e^{-|x|^2}dx$ for all $x\in{\mathbb R}^n$ be the Gauss measure on ${\mathbb R}^n$. In this paper, the authors establish the characterizations of the space BMO$(γ)$ of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order $β$ is bounded from $L^p(γ)$ to $L^{p/(1-pβ)}(γ)$, or from the Hardy space $H^1(γ)$ of Mauceri and Meda to $L^{1/(1-β)}(γ)$ or from $L^{1/β}(γ)$ to BMO$(γ)$, where $β\in(0, 1)$ and $p\in(1, 1/β)$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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