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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 4

A Balakrishnan-Rubin type hypersingular integral operator and inversion of Flett potentials

Sinem Sezer Evcan(AKDENIZ UNIVERSITY)0000-0003-2066-7833
Melih Eryiğit(AKDENIZ UNIVERSITY)0000-0002-9782-7199
Selim Çobanoğlu(Ahi Evran Vocational and Technical Anatolian High School)0000-0003-0566-5258
Pages
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Publication Date
2020-08-06
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In the present paper we introduce new ``truncated" hypersingular integral operators $D_{\epsilon}^{\alpha}f,(\epsilon>0)$ generated by the modified Poisson semigroup and obtain an explicit inversion formula for the Flett potentials in framework of $L_p$--spaces. **************************************************************************************************************************************************** ****************************************************************************************************************************************************

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Objective & Hypothesis:In the present paper we introduce new ``truncated" hypersingular integral operators $D_{\epsilon}^{\alpha}f,(\epsilon>0)$ generated by the modified Poisson semigroup and obtain an explicit inversion formula for the Flett potentials in framework of $L_p$--spaces. **************************************************************************************************************************************************** ****************************************************************************************************************************************************
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Key Findings & Data:In the present paper we introduce new ``truncated" hypersingular integral operators $D_{\epsilon}^{\alpha}f,(\epsilon>0)$ generated by the modified Poisson semigroup and obtain an explicit inversion formula for the Flett potentials in framework of $L_p$--spaces. **************************************************************************************************************************************************** ****************************************************************************************************************************************************
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Conclusion & Impact:In the present paper we introduce new ``truncated" hypersingular integral operators $D_{\epsilon}^{\alpha}f,(\epsilon>0)$ generated by the modified Poisson semigroup and obtain an explicit inversion formula for the Flett potentials in framework of $L_p$--spaces. **************************************************************************************************************************************************** ****************************************************************************************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Flett potentials · Truncated hypersingular integrals · Poisson semigroup

Abstract

In the present paper we introduce new ``truncated" hypersingular integral operators $D_{\epsilon}^{\alpha}f,(\epsilon>0)$ generated by the modified Poisson semigroup and obtain an explicit inversion formula for the Flett potentials in framework of $L_p$--spaces. **************************************************************************************************************************************************** ****************************************************************************************************************************************************

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Cite This Article

Evcan, S. S., Eryiğit, M., Çobanoğlu, S. (2020). A Balakrishnan-Rubin type hypersingular integral operator and inversion of Flett potentials. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 4. https://doi.org/10.15672/hujms.489071

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