Sharp estimates for the $ {p} $-adic $ {m} $-linear $ {n} $-dimensional Hardy and Hilbert operators on $ {p} $-adic weighted Morrey space

Tingting Xu; Zaiyong Feng; Tianyang He; Xiaona Fan; Tingting Xu; Zaiyong Feng; Tianyang He; Xiaona Fan

doi:10.3934/math.2025630

AIMS Mathematics

2025, Volume 10, Issue 6: 14012-14031. doi: 10.3934/math.2025630

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Research article

Sharp estimates for the $ {p} $-adic $ {m} $-linear $ {n} $-dimensional Hardy and Hilbert operators on $ {p} $-adic weighted Morrey space

1.
Department of Mathematics Teaching, Nanjing Vocational Institute of Railway Technology, Nanjing 210031, China
2.
Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao 266237, China
3.
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Received: 11 February 2025 Revised: 28 May 2025 Accepted: 13 June 2025 Published: 18 June 2025
MSC : Primary 42B25; Secondary 42B20, 47B47, 47H60

In this paper, we studied the sharp bounds for the $ m $-linear $ n $-dimensional $ p $-adic integral operator with a kernel on central and noncentral $ p $-adic Morrey spaces with power weight. As an application, the sharp bounds for $ p $-adic Hardy and Hilbert operators on $ p $-adic weighted Morrey spaces were obtained. Finally, we also found the sharp bound for the $ p $-adic Hausdorff operator on $ p $-adic weighted central and noncentral Morrey spaces, which generalizes the previous results.
Citation: Tingting Xu, Zaiyong Feng, Tianyang He, Xiaona Fan. Sharp estimates for the $ {p} $-adic $ {m} $-linear $ {n} $-dimensional Hardy and Hilbert operators on $ {p} $-adic weighted Morrey space[J]. AIMS Mathematics, 2025, 10(6): 14012-14031. doi: 10.3934/math.2025630

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Abstract

In this paper, we studied the sharp bounds for the $ m $-linear $ n $-dimensional $ p $-adic integral operator with a kernel on central and noncentral $ p $-adic Morrey spaces with power weight. As an application, the sharp bounds for $ p $-adic Hardy and Hilbert operators on $ p $-adic weighted Morrey spaces were obtained. Finally, we also found the sharp bound for the $ p $-adic Hausdorff operator on $ p $-adic weighted central and noncentral Morrey spaces, which generalizes the previous results.

References

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