变量核参数型Marcinkiewicz积分算子在加权Campanato空间的有界性

doi:10.6040/j.issn.1671-9352.0.2016.037

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (10): 1-5.doi: 10.6040/j.issn.1671-9352.0.2016.037

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变量核参数型Marcinkiewicz积分算子在加权Campanato空间的有界性

黄玲玲,赵凯^*

青岛大学数学与统计学院, 山东青岛 266071

收稿日期:2016-01-25 出版日期:2016-10-20 发布日期:2016-10-17
通讯作者: 赵凯(1960— ),男,博士,教授,研究方向为调和分析及其应用. E-mail:zhkzhc@aliyun.com E-mail:18765918957@163.com
作者简介:黄玲玲(1992— ),女,硕士研究生,研究方向为调和分析及其应用. E-mail:18765918957@163.com
基金资助:
国家自然科学基金资助项目(11471176);山东省自然科学基金资助项目(BS2014SF002)

Boundedness of the parameterized Marcinkiewicz integral operators with variable kernels on weighted Campanato spaces

HUANG Ling-ling, ZHAO Kai^*

School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China

Received:2016-01-25 Online:2016-10-20 Published:2016-10-17

摘要/Abstract

摘要： 借助于带变量核参数型Marcinkiewicz积分算子的加权L^p有界性,利用经典的不等式估计以及加权Campanato空间的性质,证明了其在加权Campanato空间的有界性。作为Campanato空间的一个特例,还得到了其在加权BMO(Rⁿ)空间的有界性。

关键词: Marcinkiewicz积分算子, 加权Campanato空间, 有界性, 变量核

Abstract: Based on the results of the boundedness of parameterized Marcinkiewicz integral operators on weighted L^p spaces, by using the estimates of classical inequalities and the properties of the weighted Campanato spaces, the boundedness of the parameterized Marcinkiewicz integral operators μ^ρ_Ω with variable kernel on weighted Campanato and BMO spaces is obtained.

Key words: Marcinkiewicz integral operator, weighted Campanato space, boundedness, variable kernel

中图分类号:

O174.2

黄玲玲,赵凯. 变量核参数型Marcinkiewicz积分算子在加权Campanato空间的有界性[J]. 山东大学学报（理学版）, 2016, 51(10): 1-5.

HUANG Ling-ling, ZHAO Kai. Boundedness of the parameterized Marcinkiewicz integral operators with variable kernels on weighted Campanato spaces[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 1-5.

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变量核参数型Marcinkiewicz积分算子在加权Campanato空间的有界性

Boundedness of the parameterized Marcinkiewicz integral operators with variable kernels on weighted Campanato spaces

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