A uniform $L^{\infty}$ estimate of the smoothing operators related to plane curves In dealing with the spectral synthesis property for a plane curve with nonzero curvature, a key step is to have a uniform $L^{\infty}$ estimate for some smoothing operators related to the curve. In this paper, we will show that the same $L^{\infty}$ estimate holds true for a plane curve that may have zero curvature. Categories:42b20, 42b15