The Littlewood-Paley $g$-function in quantum calculus

Abstract

The purpose of this paper is to define
and study, by the virtue of the $q$-Hardy-Littlewood maximal
function $\mathcal{M}_q(f)$ the so called $L^p$-boundedness of the
$q$-Littlewood-Paley $g$-function when $p\in(1,2]$.