In 1949, M. Riesz [3] generalized the Riemann-Liouville integral of one-variable to high dimensional Euclidean spaces and obtained a powerful method now known as the Riesz integral for studying wave operators. In this paper we apply the Riesz integral to get the global space-time estimate parallel to u parallel to(q) less than or equal to C {parallel to w parallel to(p) + t((1-n)/(n+1))(parallel to g parallel to(p) + parallel to del(f) parallel to(p))} where 1/g = 1/p - 2/(n + 1), 1/p + 1/q = 1, and u is the solution of the Cauchy problem square u(x,t) = w(x,t) in R(+)(n+1), w/(x,0) = f(x), and partial derivative(t)u(x,0) = g(x).
