On a restriction problem of de Leeuw type for Laguerre multipliers

Abstract

In 1965 K. de Leeuw \cite{deleeuw} proved among other things in the Fourier transform setting: {\it If a continuous function $m({\xi }_1,\dots ,{\xi }_n)$ on ${\mathbf{R}}^n$ generates a bounded transformation on $L^p({\mathbf{R}}^n),1\le p\le \infty ,$ then its trace $\tilde{m}({\xi }_1,\dots ,{\xi }_m)=m({\xi }_1,\dots ,{\xi }_m,0,\dots ,0),m<n,$ generates a bounded transformation on $L^p({\mathbf{R}}^m)$. } In this paper, the analogous problem is discussed in the setting of Laguerre expansions of different orders.

References in corpus (1)

• On weighted transplantation and multipliers for Laguerre expansions