Global smoothness preservation by multivariate singular integrals


By using various kinds of moduli of smoothness, it is established that the multivariate variants of the well-known singular integrals of Picard, Poisson-Cauchy, Gauss- Weierstrass and their Jackson-type generalisations satisfy the "global smoothness preservation" property. The results are extensions of those proved by the authors for the univariate case.

Publication Title

Bulletin of the Australian Mathematical Society