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Let $u(x,y)$ be a harmonic function in the half-plane ${\mathbf{R}}_{+}^{n+1}$, $n\ge 2$. We define a family of functionals $D(u;r),-\infty \>r\>\infty$, that are analogs of the family of local times associated to the process $u(x_t,y_t)$ where $(x_t,y_t)$ is Brownian motion in ${\mathbf{R}}_{+}^{n+1}$. We show that $D\left(u\right)={sup}_{r}D(u;r)$ is bounded in $L^p$ if and only if $u(x,y)$ belongs to $H^p$, an equivalence already proved by Barlow and Yor for the supremum of the local times. Our proof relies on the theory of singular integrals due to Caldéron and Zygmund, rather than the stochastic calculus.