Hardy space estimates for the wave equation on compact Lie groups (Q609352)

The authors prove that on a compact Lie group \(G\) of dimension \(n\), the multiplier operator \(e^{is\sqrt L}(1+L)^{-\beta/2}\), \(s\in (0,1]\), where \(-L\) is the Laplacian, can be extended to a bounded operator on the Hardy space \(H^p(G),\) \(0<p<\infty\), if and only if \(|\frac1p-\frac12|\leq \frac{\beta}{n-1}\). The result is an anlogue of a well-known theorem in Euclidean space.