Decay near boundary of volume of sublevel sets of $m-$subharmonic functions

Abstract

We investigate decay near boundary of the volume of sublevel sets in Cegrell classes of m− subharmonic function on bounded domains in C n . On the reverse direction, some sufficient conditions for membership in certain Cegrell's classes, in terms of the decay of the sublevel sets, are also discussed. CONTENTS 1. Introduction 1 2. Preliminaries 3 2.1. m-complex Hessian measure 3 2.2. The averaging lemma 4 3. Proofs of the results 6 References 13