Littlewood–Paley functions associated with general Ornstein–Uhlenbeck semigroups

• Published in: Annals of functional analysis Vol. 16; no. 4
• Main Authors: Almeida, Víctor, Betancor, Jorge J., Fariña, Juan C., Quijano, Pablo, Rodríguez-Mesa, Lourdes
• Format: Journal Article
• Language: English
• Published: 01.10.2025
• ISSN: 2639-7390; 2008-8752
• DOI: 10.1007/s43034-025-00457-x

In this paper, $$L^p(\mathbb {R}^d,\gamma _\infty )$$ L p ( R d , γ ∞ ) -boundedness properties for Littlewood–Paley g-functions involving time and spatial derivatives of Ornstein–Uhlenbeck semigroups are established. Here, $$\gamma _\infty$$ γ ∞ denotes the invariant measure. To prove the strong type results for $$1<p< {\infty}$$ 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 $$L^p(\mathbb {R}^d,\gamma _\infty )$$ L p ( R d , γ ∞ ) -boundedness properties for maximal and variation operators for Ornstein–Uhlenbeck semigroups are proved.