Carleson measure

Summary

A Carleson measure is a positive measure on the unit disc with a size bound near the boundary. Its mass in each box touching the boundary is at most a constant times the length of the box. Carleson showed that these are exactly the measures $\mu$ for which the Hardy space $H^p$ embeds continuously into $L^p(\mu)$. They appear in the corona theorem, in interpolation problems and in the duality between $H^1$ and BMO.