- Turkish Journal of Mathematics
- Vol: 41 Issue: 6
- On the rate of $L_p$-convergence of Balakrishnan—Rubin-type hypersingular integrals associated to th...
On the rate of $L_p$-convergence of Balakrishnan—Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup
Authors : Melih Eryiğit, Selim Çobanoğlu
Pages : 1376-1384
View : 6 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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