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p-进中心函数空间及奇异积分算子
引用本文:吴清艳,陆善镇,傅尊伟.p-进中心函数空间及奇异积分算子[J].数学年刊A辑(中文版),2017,38(1):073-90.
作者姓名:吴清艳  陆善镇  傅尊伟
作者单位:临沂大学数学系, 山东 临沂 276005.,北京师范大学数学科学学院, 北京 100875.,通讯作者. 临沂大学数学系, 山东 临沂 276005.
基金项目:本文受到国家自然科学基金(No.11271175,No.11301248,No.11671185)的资助.
摘    要:引入了几类$p$-\!\!进中心函数空间, 包括$p$-\!\!进$A^q$和 $B^q$空间、$p$-\!\!进$\lambda$-\!\!中心BMO空间 以及$p$-\!\!进中心 Morrey空间, 得到了$p$-\!\!进$A^q$空间与 $B^q$ 空间的对偶性、$p$-\!\!进$\lambda$-\!\!中心BMO空间和中心Morrey空间的特征, 研究了这些空间与加权 $p$-\!\!进 Lebesgue 空间之间的关系. 另外, 还建立了一类奇异积分算子在$p$-\!\!进中心Morrey空间中的有界性, 更进一步, 得到了这类算子交换子 在$p$-\!\!进中心Morrey空间中的$\lambda$-\!\!中心BMO估计.

关 键 词:$p$-Adic  $lambda$-central  BMO  space    $p$-Adic  centralMorrey  space    Singular  integral  operator
收稿时间:2015/3/4 0:00:00
修稿时间:2016/4/26 0:00:00

p-Adic Central Function Spaces and Singular Integral Operators
WU Qingyan,LU Shanzhen and FU Zunwei.p-Adic Central Function Spaces and Singular Integral Operators[J].Chinese Annals of Mathematics,2017,38(1):073-90.
Authors:WU Qingyan  LU Shanzhen and FU Zunwei
Institution:Department of Mathematics, Linyi University, Linyi 276005, Shandong, China.,School of Mathematical Sciences, Beijing Normal University,Beijing 100875, China. and Corresponding author. Department of Mathematics, Linyi University,Linyi 276005, Shandong, China.
Abstract:In this paper, the authors introduce several $p$-adic central function spaces including $p$-adic $A^q$ and $B^q$ spaces, $p$-adic $\lambda$-central BMO spaces and $p$-adic central Morrey spaces. The authors get the duality of $p$-adic $A^q$ and $B^q$ spaces, the characterization of $p$-adic $\lambda$-central BMO spaces and central Morrey spaces, and study the relationship among these spaces and $p$-adic Lebesgue spaces with weights. In addition, the authors establish the boundedness of a class of singular integral operators on $p$-adic central Morrey spaces. Moreover, the $\lambda$-central BMO estimates for commutators of these singular integral operators on $p$-adic central Morrey spaces are obtained.
Keywords:$p$-Adic $lambda$-central BMO space  $p$-Adic centralMorrey space  Singular integral operator
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