Random Power Series in Qp,0 Spaces

Abstract

Aulaskari et al. proved if 0<p<1 and εn is sequence of independent, identically distributed Rademacher random variables on a probability space, then the condition Σn=0∞n1−pan2<∞ implies that the random power series Rfz=∑n=0∞anεnzn∈Qp almost surely. In this paper, we improve this result showing that the condition Σn=0∞n1−pan2<∞ actually implies Rf∈Qp,0 almost surely.