Abstract
In a recent paperIan Inglis gives some sufficient conditions for a function on a totally disconnected compact Abelian group to be anL p Fourier multiplier. His proof depends on an interpolation theorem ofE. M. Stein. In this note we prove a generalization ofInglis' theorem. Our result is deduced from a factorization theorem, the proof of which is elementary, and a standard multiplier theorem.
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