The kernels of vallee poussin type on P-adic fields

Abstract

In this paper, we present a class of approximation identity operators of convolution type on the p-acid field K and on the ring of integersD⊂K, and study their approximation properties. All the kernels of these operators are of approximation identity, and are called de la Vallee Poussin type (VP type kernels). The structure of the VP type kernels onD is essentially an analogue of the classical one, however, the approximation properties are much better. Additionally, we discuss the maximal VP type operators and their properties.