\(L^p-L^q\) multipliers on locally compact groups (Q2007978)

The authors are concerned with the \(L^p-L^q\) boundedness of spectral and Fourier multipliers on general locally compact separable unimodular groups \(G\) for the range \(1< p\leq 2\leq q<\infty\). Further, a spectral multiplier theorem on general locally compact separable unimodular groups is established. As a consequence, several embedding results are derived as well as time-asymptotics for the \(L^p-L^q\) norms of the heat kernels for general positive unbounded invariant operators on \(G\). The results obtained by the authors generalize and extend some known results in the case of sub-Laplacian operators on compact Lie groups and on the Heisenberg group.