H1 space on the unit disk
= H1 space on the unit disk
{c}
{title2=$H^1(\mathbb D)$}
This <Hardy space> consists of <holomorphic functions> with $\|f\|_1=\sup_{r<1}\int_{\partial\mathbb D}|f(r\xi)|\,dm(\xi)<\infty$, where $m$ is normalized angular measure. The <H1 non-tangential maximal inequality on the disk> controls their approach to the boundary, and the <Carleson embedding theorem on the disk> characterizes measures against which all these functions remain integrable.