Convolution estimates for some measures on flat curves (Q1177890)

Let \(\mu\) be a singular measure supported on a flat curve in the plane. It is shown that under certain conditions it holds that \(\mu*L^ \phi\subseteq L^ 2\) where \(L^ \phi\) is an Orlicz space, and the Orlicz function \(\phi\) satisfies \(\lim_{t\to \infty} \phi(t)/t^ 2=0\). Also estimates on the distribution function of the Fourier transform of \(\mu\) are obtained.