Square function characterization of weak Hardy spaces

Abstract

We obtain a new square function characterization of the weak Hardy space $H^{p,\infty}$ for all $p\in(0,\iy)$. This space consists of all tempered distributions whose smooth maximal function lies in weak $L^p$. Our proof is based on interpolation between $H^p$ spaces. The main difficulty we overcome is the lack of a good dense subspace of $H^{p,\infty}$ which forces us to work with general $H^{p,\infty}$ distributions.