In 1965 K. de Leeuw \cite{deleeuw} proved among other things in the Fourier
transform setting: {\it If a continuous function m(ξ1​,…,ξn​) on
Rn generates a bounded transformation on Lp(Rn),1≤p≤∞, then its trace m~(ξ1​,…,ξm​)=m(ξ1​,…,ξm​,0,…,0),m<n, generates a bounded transformation on Lp(Rm). } In this paper, the analogous problem is discussed in the setting of
Laguerre expansions of different orders