Harmonic majorant
= Harmonic majorant
A harmonic majorant of a real function $u$ is a real <harmonic function> $h$ with $h\geq u$ pointwise. A least harmonic majorant lies below every other harmonic majorant. A continuous <subharmonic function> need not have one: $u(z)=(1-|z|^2)^{-1}$ on the <unit disk> has increasing circular means diverging to infinity, whereas any harmonic majorant would have the same finite mean on every centered circle.