On a restriction problem of de Leeuw type for Laguerre multipliers
Authors: George Gasper and Walter Trebels
Abstract:
In [On $L^p$ multipliers, Ann. of Math. 81 (1965), 364-379]
K. de Leeuw proved among other things in the Fourier transform setting:
{\it If a continuous function $m(\xi_1, \ldots ,\xi_n)$ on ${\bf R}^n$
generates a bounded transformation on $L^p({\bf R}^n),\; 1\le p \le \infty$,
then its trace
$\tilde{m}(\xi_1, \ldots ,\xi_k)= m(\xi_1, \ldots, \xi_k,0,\ldots ,0), k < n$,
generates a bounded transformation on $L^p({\bf R}^k)$.} In this paper,
the analogous problem is discussed in
the setting of Laguerre expansions of different orders.
This article published in
Acta Math. Hungar. 68 no. 1-2 (1995), 135-149.
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