广义Morrey 空间上带变量核的Littlewood-Paley 算子

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 630-642.

广义Morrey 空间上带变量核的Littlewood-Paley 算子

(北京科技大学应用科学学院数力系 |北京 100083)；(北京师范大学数学科学学院, 数学与复杂系统教育部重点实验室北京 100875)

收稿日期:2007-09-12 修回日期:2008-12-12 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
国家自然科学基金(10571015, 10826046)和高等学校博士学科点专项科研基金(20050027025)资助

Littlewood-Paley Operator with Variable Kernel in Generalized Morrey Spaces

(Department of Mathematics and Mechanics, Applied Science School, University of Science and Technology Beijing, |Beijing 100083)；(School of Mathematics, Laboratory of Mathematics and Complex Systems (BNU) Ministry of Education, China, Beijing Normal University, Beijing 100875)

Received:2007-09-12 Revised:2008-12-12 Online:2009-06-25 Published:2009-06-25
Supported by:
国家自然科学基金(10571015, 10826046)和高等学校博士学科点专项科研基金(20050027025)资助

摘要/Abstract

摘要：

该文给出了一类带变量核的抛物型Littlewood-Paley 算子g_Φ 在广义 Morrey 空间L^p^,ω(Rⁿ)上的有界性. 作为上述结果的应用, 得到了g_Φ 与 BMO 函数 b(x)生成的交换子[b, g_Φ]在L^p^, ^ω( Rⁿ)上的有界性.

关键词: Littlewood-Paley 算子, 变量核, 交换子, Morrey空间

Abstract:

In this paper the authors study the boundedness for a class of parabolic Littlewood-Paley operator g_Φ with variable kernels in generalized Morrey spaces L^p^, ^ω(Rⁿ). As an application of the above result, the boundeness of the commutator [b, g_Φ], formed by g_Φ and a BMO(Rⁿ)function b(x) in L^p, ω(Rⁿ) is also obtained.

Key words: Littlewood-Paley operator, , Variable kernel, , Commutator, , Morrey space

中图分类号:

42B20

陈艳萍, 丁勇. 广义Morrey 空间上带变量核的Littlewood-Paley 算子[J]. 数学物理学报, 2009, 29(3): 630-642.

CHEN Yan-Ping, DING Yong. Littlewood-Paley Operator with Variable Kernel in Generalized Morrey Spaces[J]. Acta mathematica scientia,Series A, 2009, 29(3): 630-642.

参考文献

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