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 $m(\xi _1, \ldots ,\xi _n)$ on ${\bf R}^n$ generates a bounded transformation on $L^p({\bf R}^n),\; 1\le p \le \infty ,$ then its trace $\tilde{m}(\xi _1, \ldots ,\xi _m)=m(\xi _1, \ldots ,\xi _m,0,\ldots ,0), \; m<n,$ generates a bounded transformation on $L^p({\bf R}^m)$. } In this paper, the analogous problem is discussed in the setting of Laguerre expansions of different orders.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- August 1994
- DOI:
- 10.48550/arXiv.math/9408211
- arXiv:
- arXiv:math/9408211
- Bibcode:
- 1994math......8211G
- Keywords:
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- Mathematics - Classical Analysis and ODEs