  In this paper, interpolation by scaled multi-integer translates of Gaussian
kernels is studied. The main result establishes $L_p$ Sobolev error estimates
and shows that the error is controlled by the $L_p$ multiplier norm of a
Fourier multiplier closely related to the cardinal interpolant, and comparable
to the Hilbert transform. Consequently, its multiplier norm is bounded
independent of the grid spacing when $1<p<\infty$, and involves a logarithmic
term when $p=1$ or $\infty$.
