CONVOLUTION OF A MEASURE WITH ITSELF AND A RESTRICTION THEOREM

Let S-k = {(y, \y\(k)): y is an element of R(n-1)} subset of R(n) and sigma be the measure defined by [sigma,phi] = integral(Rn-1)phi(y, \y\ (k))dy. Let sigma(P) denote the measure obtained by restricting sigma to the set P = [0, infinity)(n-1). We prove estimates on sigma(P) si gma(P). As a corollary we obtain results on the restriction to S-k sub set of R(3) of the Fourier transform of functions on R(3) for k is an element of R, 2 < k < 6.