Sharp weak bounds for fractional Hardy-type operators on homogeneous groups

Hongbin Liu; Juan Zhang; Qianjun He; Hongbin Liu; Juan Zhang; Qianjun He

doi:10.3934/math.20251033

AIMS Mathematics

2025, Volume 10, Issue 10: 23292-23305. doi: 10.3934/math.20251033

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Research article

Sharp weak bounds for fractional Hardy-type operators on homogeneous groups

1.
School of Science, Beijing Forestry University, Beijing 100083, China
2.
School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received: 10 June 2025 Revised: 06 August 2025 Accepted: 01 September 2025 Published: 14 October 2025
MSC : 42B35, 47A30

In this paper, we establish weak bounds for fractional Hardy operators on central Morrey spaces within the framework of homogeneous groups. We provide precise operator norms and investigate weak bounds for Hardy operators on central Morrey spaces with power weights. These results significantly extend previous findings in the study of Hardy-type operators and contribute to a broader understanding of their behavior in more general settings, particularly within homogeneous groups.
- homogeneous group,
- fractional Hardy-type operators,
- sharp weak bounds,
- central Morrey spaces,
- weighted estimates
Citation: Hongbin Liu, Juan Zhang, Qianjun He. Sharp weak bounds for fractional Hardy-type operators on homogeneous groups[J]. AIMS Mathematics, 2025, 10(10): 23292-23305. doi: 10.3934/math.20251033

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Abstract

In this paper, we establish weak bounds for fractional Hardy operators on central Morrey spaces within the framework of homogeneous groups. We provide precise operator norms and investigate weak bounds for Hardy operators on central Morrey spaces with power weights. These results significantly extend previous findings in the study of Hardy-type operators and contribute to a broader understanding of their behavior in more general settings, particularly within homogeneous groups.

References

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