Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution

Mohammed Ali; Qutaibeh Katatbeh; Oqlah Al-Refai; Basma Al-Shutnawi; Mohammed Ali; Qutaibeh Katatbeh; Oqlah Al-Refai; Basma Al-Shutnawi

doi:10.3934/math.20241085

AIMS Mathematics

2024, Volume 9, Issue 8: 22287-22300. doi: 10.3934/math.20241085

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Research article

Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution

1.
Department of Mathematics and Statistics, Faculty of Science and Arts, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
2.
Department of Mathematics, Zarqa University, Zarqa 13132, Jordan
3.
Department of mathematics, Faculty of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, Jordan

Received: 09 May 2024 Revised: 03 July 2024 Accepted: 10 July 2024 Published: 17 July 2024
MSC : 42B20, 42B25

In this paper, specific $ L^p $ estimates for generalized Marcinkiewicz operators correlated to surfaces of revolution are proved. These estimates and the extrapolation procedure of Yano are employed to confirm the $ L^p $ boundedness of the above-mentioned integrals under weaker assumptions on the singular kernels. Our findings generalize and improve several known results.
- Triebel-Lizorkin space,
- singular kernels,
- generalized Marcinkiewicz integrals,
- $ L^p $ estimates,
- extrapolation
Citation: Mohammed Ali, Qutaibeh Katatbeh, Oqlah Al-Refai, Basma Al-Shutnawi. Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution[J]. AIMS Mathematics, 2024, 9(8): 22287-22300. doi: 10.3934/math.20241085

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Abstract

In this paper, specific $ L^p $ estimates for generalized Marcinkiewicz operators correlated to surfaces of revolution are proved. These estimates and the extrapolation procedure of Yano are employed to confirm the $ L^p $ boundedness of the above-mentioned integrals under weaker assumptions on the singular kernels. Our findings generalize and improve several known results.

References

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