Vol. 30, No. 1, 1969

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Singular integrals in several variables over a local field

Keith Lowell Phillips and Mitchell Herbert Taibleson

Vol. 30 (1969), No. 1, 209–231
Abstract

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

Lf =  lim ψk ∗f,
k→ ∞

where the kernel ψk vanishes in a neighborhood of 0,

∫
|x|=1 ψk(x)dx = 0,

and ψk satisfies certain smoothness conditions.

Mathematical Subject Classification
Primary: 47.70
Secondary: 42.00
Milestones
Received: 10 April 1968
Published: 1 July 1969
Authors
Keith Lowell Phillips
Mitchell Herbert Taibleson