大Herz-Morrey空间上Marcinkiewicz积分算子高阶对易子的BMO估计

Babar SULTAN, Mehvish SULTAN, Ferit GÜRBÜZ
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引用次数: 0

摘要

设$\mathbb{S}^{n-1}$用归一化勒贝格测度表示$\mathbb{R}^n$中的单位球。设$\Phi\in L^{r}(\mathbb{S}^{n-1})$是零次齐次函数,$b$是$\mathbb{R}^n$上的一个局部可积函数。本文定义了Marcinkiewicz积分$[b,\mu_{\Phi}]^m$的高阶对易子,并在大变量Herz-Morrey空间$M\dot{K}^{\alpha(.),\beta}_{u,v(.)}(\mathbb{R}^n)$上证明了$[b,\mu_{\Phi}]^m$的有界性。
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BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand Herz-Morrey spaces
Let $\mathbb{S}^{n-1}$ denote the unit sphere in $\mathbb{R}^n$ with the normalized Lebesgue measure. Let $\Phi\in L^{r}(\mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $\mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,\mu_{\Phi}]^m$ and prove the boundedness of $[b,\mu_{\Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $M\dot{K}^{\alpha(.),\beta}_{u,v(.)}(\mathbb{R}^n)$.
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