Integral mean δ-subharmonic functions and classes of almost regularly increasing

Abstract

Classes $\Lambda_\delta$ of functions of finite $\lambda$-type $\delta$-subharmonic in $\mathbb R^m$ are investigated. A membership criterion that defines when a function belongs to the class $\Lambda_\delta$ expressed in terms of its integral q-means is established. Classes of entirely regular growth of functions that are $\delta$-subharmonic in $\mathbb R^m$ are introduced and the behavior of these functions at infinity and the distribution of  Riesz-associated measures are studied.