Singular integrals in several variables over a local field

Keith Lowell Phillips and Mitchell Herbert Taibleson

Vol. 30 (1969), No. 1, 209–231

DOI: 10.2140/pjm.1969.30.209

Abstract

In this paper we construct singular integral transforms of the Calderón-Zygmund type for K^d where K is a nondiscrete zero dimensional locally compact field and d is a positive integer. The transforms have the form

where the kernel ψ_k vanishes in a neighborhood of 0,

and ψ_k satisfies certain smoothness conditions.

Mathematical Subject Classification

Primary: 47.70

Secondary: 42.00

Milestones

Received: 10 April 1968

Published: 1 July 1969