APPLICATION OF NORMAL FAMILY OF a-SUBHARMONIC FUNCTIONS TO THE EDREI-FUCHS ELLIPSE THEOREM

Abstract

In this paper we study the asymptotic behaviour affunctions extremal
for the well known inequality introduced by Edrei-Fuchs (called the Ellipse Theorem) by considering a nonnat family of a-subhannonic functions. This approach allows us to describe precisely the prototype of all functions extremal for the Edrei-Fuchs ellipse theorem. Indeed, it turns out that the functions which are extremal for the Edrei-Fuchs
inequality are also extremal for the inequality introduced by Essen-Rossi-Shea.