A note on \(L^p\)-\(L^q\) boundedness of Fourier multipliers on noncommutative spaces

Abstract

In this work, we study Fourier multipliers on noncommutative spaces. In particular, we show a simple proof of \(L^p\)-\(L^q\) estimate of Fourier multipliers on general noncommutative spaces associated with semifinite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.