Resumen

MORENO, Jorge; PINEDA, Ebner  y  URBINA, Wilfredo. Boundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences. Rev.colomb.mat. [online]. 2021, vol.55, n.1, pp.21-41.  Epub 04-Nov-2021. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v55n1.99097.

The main result of this paper is the proof of the boundedness of the Maximal Function T* of the Ornstein-Uhlenbeck semigroup {T t } t≥0 in ℝ d , on Gaussian variable Lebesgue spaces L p(·) (γ d ), under a condition of regularity on p(·) following [5] and [8]. As an immediate consequence of that result, the Lp(·)(γ d )-boundedness of the Ornstein-Uhlenbeck semigroup {T t } t≥0 in ℝ d is obtained. Another consequence of that result is the Lp(·)(γ d )-boundedness of the Poisson-Hermite semigroup and the Lp(·)(γ d )-boundedness of the Gaussian Bessel potentials of order β > 0.

Palabras clave : Gaussian harmonic analysis; variable Lebesgue spaces; Ornstein-Uhlenbeck semigroup.

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