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几类交换子在广义Morrey空间上的估计 被引量：1

Estimate of Some Kind of Commutators on Generalized Morrey Spaces
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摘要 设ω_i(x,r)(i=1,2)是R^n×R^+上的可测正函数,当(ω_1,ω_2)∈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L^(P,ω_1)(R^n)到L^(p,ω_2)(R^n)的有界算子.对于奇异积分算子T以及Riesz积分位势算子I_α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. Let wi（x, r） （i = 1, 2） be a positive measurable function in Rn x R＋. If （wl, w2） C S0,n, then the commutators generated by the BMO function and maximal operators M are bounded from Lp,ω1 （Rn） to Lp,ω2 （Rn）. Similarly, the commutators generated by the singular integral operator T and the Riesz potential operator Is are also bounded on generalized Morrey spaces. All the results generalize the corresponding results of Mizuhara on the generalized Morrey spaces.
作者 叶晓峰
机构地区 华东交通大学数学与信息科学系
出处 《数学年刊（A辑）》 CSCD 北大核心 2012年第3期375-382,共8页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.10961015 No.11161021)资助的项目
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 Commutator, Singular integral operator, Maximal operator, Rieszpotential operator, Generalized Morrey space
分类号 O177 [理学—基础数学]
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参考文献11

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同被引文献13

  • 1周民强.调和分析讲义[M].北京：北京大学出版社,1999..
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  • 5Komori Y, Shirai S. Weighted Morrey spaces and a singular integral operator[J]. Math Nachr, 2009, 282(2) :219-231.
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  • 7Nakai E. Hardy-Littlewood maximal operators, singular in- tegral operators and Riesz potential on Morrey space [J]. Math Nachr, 1994, 166 ( 1 ) : 95-103.
  • 8Akbulut A, Gulieve V, Mustufaver R. Boundedness of maximal operators on Morrey space with generalized growth functions[EB/OL]. (2010-01-26)[2010-11-28] http://www. math. cas. cz/preprint/pre- 210/pdf.
  • 9Grafakos L, Torres R. Multilinear Calder6n-Zygmund the- ory[J ]. Adv Math, 2002, 165 (1) : 124-164.
  • 10Grafakos L, Torres R. Maximal operator and weighted norm inequalities for multilinear singular integrals [J]. In- diana U Math J, 2002, 51:1261-1276.

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数学年刊（A辑）
2012年 第3期

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