On a restriction problem of de Leeuw type for Laguerre multipliers (Q1897830)

It is shown that for some conditions on \(\alpha\), \(\beta\) and \(p\), if \(\{m_k \}\) \((k\in \mathbb{N}_0)\) generates a bounded transformation with respect to Laguerre functions of order \(\alpha\) on some \(L^p\)-space, then it also generates a corresponding bounded transformation with respect to a Laguerre function expansion of order \(\beta\).