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

Besma Amri, Lakhdar T. Rachdi

Abstract


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].

Keywords


Riemann-Liouville operator; Fourier transform; Gauss semigroup; Poisson semigroup; Littlewood-Paley g-function

Mathematics Subject Classification


43A32; 42B25

References


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