Littlewood–Paley functions associated with general Ornstein–Uhlenbeck semigroups

In this paper, Lᵖ(Rᵈ,γ _∞ ) L p ( R d , γ ∞ ) -boundedness properties for Littlewood–Paley g-functions involving time and spatial derivatives of Ornstein–Uhlenbeck semigroups are established. Here, γ _∞ γ ∞ denotes the invariant measure. To prove the strong type results for 1<p< ∞ 1 < p < ∞ , we use R -boundedness. The weak type (1,1) property is established by studying separately global and local operators defined for the Littlewood–Paley g-functions. By the way Lᵖ(Rᵈ,γ _∞ ) L p ( R d , γ ∞ ) -boundedness properties for maximal and variation operators for Ornstein–Uhlenbeck semigroups are proved.