Heisenberg群上的分数次Hardy算子在混合范空间上的最佳界

王泽群, 魏明权, 张兴松, 燕敦验

数学学报 ›› 2021, Vol. 64 ›› Issue (5) : 811-820.

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数学学报 ›› 2021, Vol. 64 ›› Issue (5) : 811-820. DOI: 10.12386/A2021sxxb0068
论文

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4
作者信息 +

Sharp Constants on Mixed Norm Spaces for Fractional Hardy Operators on Heisenberg Group

    Ze Qun WANG1, Ming Quan WEI2, Xing Song ZHANG3, Dun Yan YAN4
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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Lp(Hn)→Lq(Hn)和L1(Hn)→Lq,∞(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.

Abstract

In this paper, studies sharp constants for fractional Hardy operators on Heisenberg group. We first give the Lp(Hn)→Lq(Hn) and L1(Hn)→Lq,∞(Hn) norm for fractional Hardy operators on Heisenberg group. Based on theses results, we further obtain the sharp constants for fractional Hardy operators on Heisenberg group of product type on mixed norm spaces.

关键词

分数次 Hardy 算子 / 混合范空间 / Heisenberg 群 / 最佳界

Key words

fractional Hardy operator / mixed norm space / Heisenberg group / sharp constant

引用本文

导出引用
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. 数学学报, 2021, 64(5): 811-820 https://doi.org/10.12386/A2021sxxb0068
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 https://doi.org/10.12386/A2021sxxb0068

参考文献

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基金

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(南湖学者奖励计划)青年项目;河南省高等学校重点科研项目(18A110028)

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