On the rate of $L_p$-convergence of Balakrishnan—Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup

Authors: MELİH ERYİĞİT, SELİM ÇOBANOĞLU

Abstract: We introduce a family of Balakrishnan—Rubin-type hypersingular integrals depending ona parameter $\varepsilon$ and generated by the Gauss—Weierstrass semigroup. Then the connection between the order of $L_p$—smoothness of a $L_p$—function $\varphi$and the rate of $L_p$-convergence of these families to $\varphi$, as $\varepsilon$ tends to 0, is obtained.

Keywords: Riesz potentials, Bessel potentials, truncated hypersingular integrals, rate of convergence, Gauss--Weierstrass semigroup

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