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We study the \(L^p\) norm of the Fourier transform of \(S_t\!f\), where \(S_t\) is a splitting operator. If \(m\) is a Fourier multiplier, we also study the operator norm of \(S_t m\). Most of our results assume \(p\) is an even integer. They are often stronger when \(f\) or \(m\) has compact support.

Split functions, Fourier transforms and multipliers