If ${p(cdot): mathbb{R}^{n} {rightarrow} (0,infty), ngeq 3}$ , is globally log-Hölder continuous and its infimum p ^? and its supremum p ⁺ are such that ${frac{n}{n-1} < p^{-} leq p^{+} < p^{-} (n-1)}$ , then the spherical maximal operator (integral averages taken with respect to the (n ? 1)-dimensional surface measure) is bounded. When n = 3, the result is then interpreted as the preservation of the integrability properties of the initial velocity of propagation to the solution of the initial-value problem for the wave equation.