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Revista Colombiana de Matemáticas
versión impresa ISSN 0034-7426
Rev.colomb.mat. vol.55 no.1 Bogotá ene./jun. 2021 Epub 04-Nov-2021
https://doi.org/10.15446/recolma.v55n1.99097
Original articles
Boundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences
Acotación de la Función Maximal del Semigrupo de Ornstein-Uhlenbeck en Espacios de Lebesgue Variables y sus consecuencias
1 Universidad Centro Occidental Lisandro Alvarado, Barquisimeto, Venezuela
2 Escuela Superior Politécnica del Litoral, Guayaquil, Ecuador
3 Roosevelt University, Chicago, USA
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.
Keywords: Gaussian harmonic analysis; variable Lebesgue spaces; Ornstein-Uhlenbeck semigroup
El principal resultado de este artículo es la prueba de la acotación de la Función Maximal T* del semigrupo de Ornstein-Uhlenbeck {T t } t≥0 en ℝ d sobre espacios de Lebesgue variables respecto de la medida Gaussiana L p(·) (γ d ), asumiendo una condición de regularidad en p(·) siguiendo [5] y [8]. Como consecuencia inmediata de éste resultado se obtiene la acotación- L p(·) (γ d ) del semigrupo de Ornstein-Uhlenbeck {T t } t≥0 en ℝ d . Otras consecuencias del resultado es la acotación L p(·) (γ d ) del semigrupo Poisson-Hermite y la acotación L p(·) (γ d ) de los potenciales de Bessel Gaussianos de orden β > 0.
Palabras clave: Análisis Armónico Gaussiano; espacios de Lebesgue Gaussianos; semigrupo de Ornstein-Uhlenbeck
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Received: June 22, 2020; Accepted: February 11, 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
