  We give a characterization of $L^{p}(\sigma)$ for uniformly rectifiable
measures $\sigma$ using Tolsa's $\alpha$-numbers, by showing, for $1<p<\infty$
and $f\in L^{p}(\sigma)$, that
  \[
  \lVert f\rVert_{L^{p}(\sigma)}\sim \left\lVert\left(\int_{0}^{\infty}
\left(\alpha_{f\sigma}(x,r)+|f|_{x,r}\alpha_{\sigma}(x,r)\right)^2\
\frac{dr}{r} \right)^{\frac{1}{2}}\right\rVert_{L^{p}(\sigma)}.
  \]
