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

S.E. Sinem (Akdeniz University, Antalya),
E. Melih (Akdeniz University, Antalya),
Ç. Selim (A.E.V.T.A. High School Urfa),


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.


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

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