L-p-L-q estimates for convolution operators with n-dimensional singular measures

Let S subset of Rn+1 be the graph of the function phi : [-1, 1](n) --> R defined by phi (x(1),..., x(n)) = Sigma(j=1)(n) \x(j)\(alpha j), with 1 < alpha(1) less than or equal to...less than or equal to alpha(n), let sigma the Euclidean area measure on S. In this article we study the L-p - L-q boundedness of convolution operators with the singular Borel measure on Rn+1 given by mu (E) = sigma (E boolean AND S).