Mixed radial-angular bounds for Hardy-type operators on Heisenberg group

Zhongci Hang; Dunyan Yan; Xiang Li; Zhongci Hang; Dunyan Yan; Xiang Li

doi:10.3934/math.20231070

AIMS Mathematics

2023, Volume 8, Issue 9: 21022-21032. doi: 10.3934/math.20231070

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Research article Special Issues

Mixed radial-angular bounds for Hardy-type operators on Heisenberg group

1.
School of Science, Shandong Jianzhu University, Jinan, 250101, China
2.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

Received: 28 April 2023 Revised: 19 June 2023 Accepted: 20 June 2023 Published: 30 June 2023
MSC : Primary 42B25; Secondary 42B20, 47H60, 47B47

In this paper, we study $ n $-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg group and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $ n $-dimensional weighted Hardy operator and weighted Cesàro operator are also obtained.
- Hardy operator,
- dual operator,
- weighted Hardy operator,
- weighted Cesàro operator,
- mixed radial-angular space,
- Heisenberg group
Citation: Zhongci Hang, Dunyan Yan, Xiang Li. Mixed radial-angular bounds for Hardy-type operators on Heisenberg group[J]. AIMS Mathematics, 2023, 8(9): 21022-21032. doi: 10.3934/math.20231070

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Abstract

In this paper, we study $ n $-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg group and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $ n $-dimensional weighted Hardy operator and weighted Cesàro operator are also obtained.

References

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