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

First, we study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator. Next, we dene and study the Littlewood-Paley g-function associated with the Riemann-Liouville operator for which we prove the Lp-boundedness for p ∈ ]1, 2].