The restriction theorem for the Grushin operators
Abstract
We study the Grushin operators acting on $\mathbb{R}^{d_1}_x \times \mathbb{R}^{d_2}_t$ and defined by the formula \begin{equation*} L=\overset{d_1}{\underset{j=1}{\sum}}\partial_{x_j}^2\left(\overset{d_1}{\underset{j=1}{\sum}}x_j^2\right)\overset{d_2}{\underset{k=1}{\sum}}\partial_{t_k}^2. \end{equation*} We establish a restriction theorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. Muller.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5298
 Bibcode:
 2014arXiv1402.5298L
 Keywords:

 Mathematics  Functional Analysis;
 42C;
 42C10;
 43A90