On rough generalized Marcinkiewicz integrals along surfaces of revolution on product spaces

Mohammed Ali; Hussain Al-Qassem; Mohammed Ali; Hussain Al-Qassem

doi:10.3934/math.2024233

AIMS Mathematics

2024, Volume 9, Issue 2: 4816-4829. doi: 10.3934/math.2024233

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On rough generalized Marcinkiewicz integrals along surfaces of revolution on product spaces

Mohammed Ali ¹,
Hussain Al-Qassem ^{2
,
,}

1.
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
2.
Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar

Received: 12 November 2023 Revised: 10 January 2024 Accepted: 12 January 2024 Published: 22 January 2024
MSC : 42B20, 42B25, 42B35

In this paper, we prove the $ L^p $ boundedness of generalized Marcinkiewicz operators along surfaces of revolution on product spaces under very weak conditions on the the singular kernels. Our results generalize and improve many previously known results.
- singular kernels,
- Marcinkiewicz integrals,
- generalized Marcinkiewicz,
- product domains,
- surfaces of revolution
Citation: Mohammed Ali, Hussain Al-Qassem. On rough generalized Marcinkiewicz integrals along surfaces of revolution on product spaces[J]. AIMS Mathematics, 2024, 9(2): 4816-4829. doi: 10.3934/math.2024233

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Abstract

In this paper, we prove the $ L^p $ boundedness of generalized Marcinkiewicz operators along surfaces of revolution on product spaces under very weak conditions on the the singular kernels. Our results generalize and improve many previously known results.

References

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