| 叶晓峰.几类交换子在广义Morrey空间上的估计[J].数学年刊A辑,2012,33(3):375~382 |
| 几类交换子在广义Morrey空间上的估计 |
| Estimate of Some Kind of Commutators on Generalized Morrey Spaces |
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| DOI： |
| 中文关键词: 交换子 奇异积分算子 极大算子 Riesz积分位势算子 广义Morrey空间 |
| 英文关键词:Commutator, Singular integral operator, Maximal operator, Riesz
potential operator, Generalized Morrey space |
| 基金项目:国家自然科学基金 |
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| 中文摘要: |
| 设ωi(x,T)(i=1,2)是Rn×R+上的可测正函数,当(ω1,ω2)∈So,n时,由BMO函数与极大算子M生成的交换子,是从广义Morrey空间Lp,ω1(Rn)到Lp,ω2(Rn)的有界算子.对于奇异积分算子T以及Riesz积分位势算子Iα生成的交换子,也得到了相似的有界性结果.该结论推广了Mizuhara在广义Morrey空间上的相关结论. |
| 英文摘要: |
| Let $\omega_{i}(x,r)\ (i=1,2)$ be a positive measurable function
in $\mathbb{R}^{n}\times \mathbb{R}^{+}$. If $(\omega_{1},\omega_{2})\in {\mathcal{S}}_{0,n}$,
then the commutators generated by the BMO function and maximal operators $M$ are bounded from $L^{p,\omega_{1}}(\mathbb{R}^{n})$
to $L^{p,\omega_{2}}(\mathbb{R}^{n})$. Similarly, the commutators generated by the singular integral operator $T$ and the Riesz potential operator
$I_\alpha$ are also bounded on generalized Morrey spaces. All the results generalize the corresponding results of Mizuhara on
the generalized Morrey spaces. |
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