Vol. 59, No. 2, 1975

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Classification of singular integrals over a local field

Charles P. Downey

Vol. 59 (1975), No. 2, 417–426
Abstract

The singular integral operators over a local field K whose kernels are multiplicative characters of the unit sphere of K are shown to be precisely those continuous operators on 2(K) which commute with translation and dilation, anticommute with an appropriately defined rotation, and whose multipliers satisfy a smoothness condition. The characterization is analogous to that of the Hilbert transform over the real numbers.

Mathematical Subject Classification 2000
Primary: 44A25
Secondary: 43A70
Milestones
Received: 14 October 1974
Revised: 12 April 1975
Published: 1 August 1975
Authors
Charles P. Downey