\(L^ p\) estimates for bi-invariant operators on classical groups (Q1352466)

Let \(G\) be a compact Lie group and \(\widehat G\) a maximal collection of inequivalent irreducible unitary representations of \(G\). A sufficient condition for \(\{m(\lambda)\}_{\lambda\in\widehat G}\) to be a multiplier for \(L^p(G)\) \((1<p<\infty)\) is known when \(\dim G=N\) and \(\nu\) is the smallest even integer such that \(2\nu>N\). The author gives a similar sufficient condition when \(G\) is a classical group with dimension \(N\) and \(\nu\) is the smallest integer such that \(2\nu>N\). The classical (compact Lie) groups consist of the unitary group \(U(n)\), the rotation group \(SO(n)\) and the unitary symplectic group \(USP(2n)\).