= Hardy space
{c}
{title2=$H^p$}
{wiki}
For $0<p<∞$, an analytic <Hardy space> controls the integral means of a <holomorphic function> as it approaches a domain boundary. On the disk, $H^p$ requires $\sup_{0<r<1}\int|F(re^{i\theta})|^p\,d\theta<\infty$; on the upper half-plane it requires $\sup_{y>0}\int_{\mathbb R}|f(x+iy)|^p\,dx<\infty$. For $p=\infty$ use a supremum norm. These analytic spaces differ from the <harmonic Hardy space of the upper half-space>; the <Hardy space of the circle> is the boundary Hilbert-space realization of the disk $H^2$ space.
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