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arXiv · 2201.13076

Maximal operator, Littlewood-Paley functions and variation operators associated with nonsymmetric Ornstein-Uhlenbeck operators

Víctor Almeida·Jorge J. Betancor·Pablo Quijano·Lourdes Rodríguez-Mesa
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Abstract

In this paper we establish $L^p$ boundedness properties for maximal operators, Littlewood-Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with nonsymmetric Ornstein-Uhlenbeck operators. We consider the Ornstein-Uhlenbeck operators defined by the identity as the covariance matrix and having a drift given by the matrix $-\lambda (I+R)$, being $\lambda >0$ and $R$ a skew-adjoint matrix. The semigroup associated with these Ornstein-Uhlenbeck operators are the basic building blocks of all normal Ornstein-Uhlenbeck semigroups.

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Víctor Almeida, Jorge J. Betancor, Pablo Quijano, Lourdes Rodríguez-Mesa. 2022-01-31. Maximal operator, Littlewood-Paley functions and variation operators associated with nonsymmetric Ornstein-Uhlenbeck operators. https://arxiv.org/abs/2201.13076

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