The Littlewood-Paley g-function associated with the Riemann-Liouville operator

Abstract

First, we study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator. Next, we define and study the Littlewood- Paley $g$-function associated with the Riemann-Liouville operator for which we prove the $L^p$-boundedness for $p ∊ |1,2|$.