Heisenberg群上的分数次Hardy算子在混合范空间上的最佳界

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Heisenberg群上的分数次Hardy算子在混合范空间上的最佳界王泽群¹, 魏明权², 张兴松³, 燕敦验⁴1. 东北财经大学数据科学与人工智能学院大连 116025;
2. 信阳师范学院数学与统计学院信阳 464000;
3. 中国人民大学附属中学朝阳学校北京 100028;
4. 中国科学院大学数学科学学院北京 100049 Sharp Constants on Mixed Norm Spaces for Fractional Hardy Operators on Heisenberg Group Ze Qun WANG¹, Ming Quan WEI², Xing Song ZHANG³, Dun Yan YAN⁴1. School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian 116025, P. R. China;
2. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China;
3. RDFZ Chaoyang School, Beijing 100028, P. R. China;
4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China

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摘要本文研究Heisenberg群上的分数次Hardy算子的最佳界.我们首先给出Heisenberg群上的分数次Hardy算子的L^p（Hⁿ）→L^q（Hⁿ）和L¹（Hⁿ）→L^q，∞（Hⁿ）最佳界.在此基础上，进一步求出一类Heisenberg群上的乘积型分数次Hardy算子在混合范空间上的最佳界.

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收稿日期: 2020-04-20

MR (2010):

O174.2

基金资助:国家自然科学基金资助项目（11471309，11561062）；河南省自然科学基金（202300410338）；信阳师范学院（南湖****奖励计划）青年项目；河南省高等学校重点科研项目（18A110028）

通讯作者:魏明权,E-mail:weimingquan11@mails.ucas.ac.cnE-mail: weimingquan11@mails.ucas.ac.cn

作者简介: 王泽群,E-mail:wangzequn17@mails.ucas.ac.cn;张兴松,E-mail:zhangxingsong17@mails.ucas.ac.cn;燕敦验,E-mail:ydunyan@ucas.ac.cn

引用本文:

王泽群, 魏明权, 张兴松, 燕敦验. Heisenberg群上的分数次Hardy算子在混合范空间上的最佳界[J]. 数学学报, 2021, 64(5): 811-820. Ze Qun WANG, Ming Quan WEI, Xing Song ZHANG, Dun Yan YAN. Sharp Constants on Mixed Norm Spaces for Fractional Hardy Operators on Heisenberg Group. Acta Mathematica Sinica, Chinese Series, 2021, 64(5): 811-820.

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http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2021/V64/I5/811

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