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.

DOI

10.3906/mat-1610-105

Keywords

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

First Page

1376

Last Page

1384

Recommended Citation

ERYİĞİT, M, & ÇOBANOĞLU, S (2017). On the rate of $L_p$-convergence of Balakrishnan—Rubin-type hypersingular integrals associated to the Gauss-Weierstrass semigroup. Turkish Journal of Mathematics 41 (6): 1376-1384. https://doi.org/10.3906/mat-1610-105