Hardy–Littlewood maximal operators and Hausdorff operators on $ p $-adic block spaces with variable exponents

Pham Thi Kim Thuy; Kieu Huu Dung; Pham Thi Kim Thuy; Kieu Huu Dung

doi:10.3934/math.20241121

AIMS Mathematics

2024, Volume 9, Issue 8: 23060-23087. doi: 10.3934/math.20241121

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Research article

Hardy–Littlewood maximal operators and Hausdorff operators on $ p $-adic block spaces with variable exponents

Pham Thi Kim Thuy ¹,
Kieu Huu Dung ^{2
,
,}

1.
Department of Mathematics, FPT University, Hanoi, Vietnam
2.
Faculty of Fundamental Sciences, Van Lang University, Ho Chi Minh City, Vietnam

Received: 22 May 2024 Revised: 09 July 2024 Accepted: 12 July 2024 Published: 29 July 2024
MSC : 26D15, 42B25, 42B99

In this paper, we established some sufficient conditions for the boundedness of the Hardy–Littlewood maximal operators and the Hausdorff operators on $ p $-adic Herz spaces and $ p $-adic local block spaces with variable exponents. In particular, the boundedness of the $ p $-adic maximal commutator operators, the $ p $-adic Hardy–Littlewood average operators, and the $ p $-adic Hardy-Hilbert operators on such spaces was also discussed.
- Hardy–Littlewood maximal operator,
- maximal commutator operator,
- Hardy-type operators,
- Hausdorff operator,
- Herz space,
- block space,
- variable exponent,
- $ p $-adic analysis
Citation: Pham Thi Kim Thuy, Kieu Huu Dung. Hardy–Littlewood maximal operators and Hausdorff operators on $ p $-adic block spaces with variable exponents[J]. AIMS Mathematics, 2024, 9(8): 23060-23087. doi: 10.3934/math.20241121

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Abstract

In this paper, we established some sufficient conditions for the boundedness of the Hardy–Littlewood maximal operators and the Hausdorff operators on $ p $-adic Herz spaces and $ p $-adic local block spaces with variable exponents. In particular, the boundedness of the $ p $-adic maximal commutator operators, the $ p $-adic Hardy–Littlewood average operators, and the $ p $-adic Hardy-Hilbert operators on such spaces was also discussed.

References

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