带变量核分数次Marcinkiewicz积分在Hardy型空间的有界性

J4 ›› 2013, Vol. 48 ›› Issue (3): 64-72.

带变量核分数次Marcinkiewicz积分在Hardy型空间的有界性

潘亚丽1, 王信松2

1. 淮北师范大学数学科学学院, 安徽淮北 235000; 2. 天津城市建设学院基础部,天津 300384

收稿日期:2012-11-05 出版日期:2013-03-20 发布日期:2013-03-14
作者简介:潘亚丽(1981- ), 女, 讲师,硕士, 研究方向为调和分析与逼近论. Email:panlijiyang@163.com
基金资助:
国家自然科学基金资助项目(11001001);安徽省教育厅自然科学研究重点项目(2006KJ069A);安徽省高等学校省级自然科学研究项目(KJ2011B152,KJ2012B166,KJ2013A235);淮北师范大学青年科研项目(2011xqxm42);淮北师范大学校级教研项目(jy12222)

Boundedness of fractional Marcinkiewicz integrals with variable kernel on Hardy type spaces

PAN Ya-li1, WANG Xin-song2

1. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China;
2. Department of Basic, Tianjin Institute of Urban Construction, Tianjin 300384, China

Received:2012-11-05 Online:2013-03-20 Published:2013-03-14

摘要/Abstract

摘要：

证明了带变量核分数次Marcinkiewicz积分μΩ,α在Hardy空间及Herz型Hardy空间上的有界性。利用Hardy空间及Herz型Hardy空间的原子分解定理,得到了在核函数Ω满足一定条件下算子μΩ,α的H1,Lnn-α型和(Hp,Lq)型以及从Herz型Hardy空间到Herz空间的有界性结论。

关键词: 分数次Marcinkiewicz积分变量核;Hardy空间;Herz型Hardy空间

Abstract:

The boundedness of the fractional type Marcinkiewicz integrals μΩ,α with variable kernels on Hardy spaces and Herz type Hardy spaces are established. Some properties of μΩ,α which kernel satisfies certain condition are given by the atomic decomposition theorem. Also, the integral μΩ,α is an operator of type H1,Lnn-α and of type (Hp,Lq). The boundedness from Herz type Hardy spaces to Herz spaces about the integral μΩ,α are presented.

Key words: fractional Marcinkiewicz integral; variable kernels; Hardy spaces; Herz type Hardy spaces

潘亚丽1, 王信松2. 带变量核分数次Marcinkiewicz积分在Hardy型空间的有界性[J]. J4, 2013, 48(3): 64-72.

PAN Ya-li1, WANG Xin-song2. Boundedness of fractional Marcinkiewicz integrals with variable kernel on Hardy type spaces[J]. J4, 2013, 48(3): 64-72.

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