Harmonic majorant

Summary

A harmonic majorant of a function is a harmonic function that lies above it everywhere on the domain. The question whether a subharmonic function has a harmonic majorant measures how large it is near the boundary of its domain. For example, a holomorphic function $f$ on the unit disc lies in the Hardy space $H^p$ exactly when $\abs{f}^p$ has a harmonic majorant. When a harmonic majorant exists, there is a smallest one, the least harmonic majorant.