The Boundedness of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure

Abstract

The main result of this work is the proof of the boundedness of the Ornstein-Uhlenbeck semigroup $\{T_t{\}}_{t\ge 0}$ in ${\mathbb{R}}^d$ on Gaussian variable Lebesgue spaces under a condition of regularity on $p(\cdot )$ following previous papers by E. Dalmaso R. Scotto and S. Pérez. As a consequence of this result, we obtain the boundedness of Poisson-Hermite semigroup and the boundedness of the Gaussian Bessel potentials of order $\beta >0$.

References in corpus (1)

• Non Tangential Convergence for the Ornstein-Uhlenbeck Semigroup