带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 56-67.

带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性

默会霞¹, 陆善镇²

1. 北京邮电大学理学院北京 100876 2. 北京师范大学数学科学学院北京 100875

收稿日期:2013-07-15 修回日期:2014-11-24 出版日期:2015-02-25 发布日期:2015-02-25
基金资助:
国家自然科学基金(11161042, 11271175, 11471050)

Boundedness of Generalized Higher Order Commutators of Marcinkiewicz |Integrals with Variable Kernels on Herz-type Hardy Spaces

MO Hui-Xia¹, LU Shan-Zhen²

1. School of Science, Beijing University of Post and Telecommunications, Beijing 100876 2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875

Received:2013-07-15 Revised:2014-11-24 Online:2015-02-25 Published:2015-02-25

摘要/Abstract

摘要：

设 $\100dpi \inline $A$$ 是 $\100dpi \inline ${\Bbb R}^{n}$$ 上的一个 $\100dpi \inline $m$$ 阶可导函数, 且 $\100dpi \inline $D^{\gamma}A\in\dot{\Lambda}_{\beta}(0<\beta<1, |\gamma|=m),$ $\Omega(x,z)\in L^{\infty}({\Bbb R}^{n})\timesL^{s}(S^{n-1})(s\geq n/(n-\beta))$$ 是零阶齐次函数且关于变量 $\100dpi \inline $z$$ 满足消失条件.
该文证明了广义高阶Marcinkiewicz积分交换子 $\100dpi \inline $\mu_{\Omega}^{A}$$ 及其变形 $\100dpi \inline $\tilde{\mu}_{\Omega}^{A}$$ 在Herz型Hardy空间的有界性.

关键词: Marcinkiewicz 积分 , Herz型Hardy空间 , Lipschit函数空间 , 交换子

Abstract:

Let $\100dpi \inline $A$$ be a function with derivatives of order $\100dpi \inline $m$$ and $\100dpi \inline $D^{\gamma}A\in\dot{\Lambda}_{\beta}(0<\beta<1, |\gamma|=m).$$ The authors in the
paper prove that if $\100dpi \inline $\Omega(x,z)\in L^{\infty}({\Bbb R}^{n})\timesL^{s}(S^{n-1})(s\geq n/(n-\beta))$$ is homogenous of degree zero and satisfies the mean value zero condition about the variable $\100dpi \inline $z$$ , then both the generalized higher order Marcinkiewicz integral $\100dpi \inline $\mu_{\Omega}^{A}$$ and itsvariation $\100dpi \inline $\tilde{\mu}_{\Omega}^{A}$$ are bounded on Herz-type Hardy spaces.

Key words: Marcinkiewicz type integral , Herz-type Hardy space , Space of Lipschitz functions , Commutator

中图分类号:

42B20

默会霞, 陆善镇. 带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性[J]. 数学物理学报, 2015, 35(1): 56-67.

MO Hui-Xia, LU Shan-Zhen. Boundedness of Generalized Higher Order Commutators of Marcinkiewicz |Integrals with Variable Kernels on Herz-type Hardy Spaces[J]. Acta mathematica scientia,Series A, 2015, 35(1): 56-67.

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