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.
ERYİĞİT, MELİH and ÇOBANOĞLU, SELİM
"On the rate of $L_p$-convergence of Balakrishnan—Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup,"
Turkish Journal of Mathematics: Vol. 41:
6, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss6/2