The author proves a uniform Fourier decay and convolution estimate for curves in the plane. Specifically, if is such that and , on , and , and is the measure on the graph given by , then the author establishes the convolution estimate
for an absolute constant (independent of ), a well as the Fourier decay estimate
for all and . The weight is not completely optimal; the author conjectures it should be replaced by the affine curvature weight . The methods are mostly elementary.