arXiv 2202.061362022-02math.CAmath.FA

Littlewood-Paley functions associated with general Ornstein-Uhlenbeck semigroups

Víctor Almeida, Jorge J. Betancor, Juan C. Fariña, Pablo Quijano, Lourdes Rodríguez-Mesa

备注：: This is a revised version of the preliminary one arXiv:2202.06136v1

英文摘要：

In this paper we establish $L^p(\mathbb{R}^d,γ_\infty)$-boundedness properties for square functions involving time and spatial derivatives of Ornstein-Uhlenbeck semigroups. Here $γ_\infty$ denotes the invariant measure. In order to prove the strong type results for $1<p<\infty$ we use $R$-boundedness. The weak type (1,1) property is established by studying separately global and local operators defined for the square Littlewood-Paley functions. By the way we prove $L^p(\mathbb{R}^d,γ_\infty)$-boundedness properties for maximal and variation operators for Ornstein-Uhlenbeck semigroups.

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