Harmonic Hardy space of the upper half-space
= Harmonic Hardy space of the upper half-space
{title2=$h^1(H^{d+1})$}
For the upper half-space $H^{d+1}=\mathbb R^d\times(0,\infty)$, this is the space of <harmonic functions> with finite <norm> $\|u\|_{h^1}=\sup_{t>0}\int_{\mathbb R^d}|u(x,t)|\,dx$. It differs from an analytic <Hardy space>: no <holomorphic function> condition is imposed, and its boundary object can be a singular finite <Borel measure>.