ESTIMATES FOR RADIAL SOLUTIONS TO THE WAVE EQUATION

We consider the Cauchy problem for the wave equation with null initial position and radial initial velocity psi. With the solution u of this problem we define the operator S(psi) = sup(t>0) t(-1) vertical bar u(x, t)vertical bar. Using simple one-dimensional operators to bound pointwise the operator S we obtain weighted L-p estimates with power weights. Even for the unweighted estimates the result for dimension higher than 3 differs from the one with general functions.