The Rate of Convergence of Truncated Hypersingular Integrals Generated by the Generalized Poisson Semigroup

S.E. Sinem; E. Melih; Ç. Selim

doi:10.15421/242004

The Rate of Convergence of Truncated Hypersingular Integrals Generated by the Generalized Poisson Semigroup

S.E. Sinem (Akdeniz University, Antalya), https://orcid.org/0000-0003-2066-7833
E. Melih (Akdeniz University, Antalya), https://orcid.org/0000-0002-9782-7199
Ç. Selim (A.E.V.T.A. High School Urfa), https://orcid.org/0000-0003-0566-5258

Abstract

We introduce a family of Balakrishnan-Rubin type hypersingular integrals depending on a parameter $$$\varepsilon $$$ and generated by the Generalized Poisson semigroup. Then the rate of convergence of these families of truncated hypersingular integrals, which converge to $$$L_{p,\nu }$$$--function $$$\varphi $$$ as $$$\varepsilon $$$ tends to $$$0$$$, is obtained.

Keywords

Flett potentials; truncated hypersingular integrals; rate of convergence; generalized Poisson semigroup

MSC 2020

26A33; 41A35; 44A35

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