Application of Normal Family to the Spread Inequality and the Paley Type Inequality

Abstract

In this paper we derive a Paley type inequality for subharmonic functions of order λ,0 < λ≤½ and describe the asymptotic behaviour of the extremal functions near Pòlya peaks. We also give an alternative proof for the spread inequality using a non-asymptotic method via - a normal family of δ -subharmonic functions.