On the constant in a transference inequality for the vector-valued Fourier transform

Abstract

The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.

An alternative proof of the main result for the special case that the parameter r is integral, due to Tom Koornwinder, has been included