arXiv subjects

Guillermo Flores

Publications and source records attributed to Guillermo Flores.

3 recordsLinked to original sources

arXiv2026

Lebesgue points of measures and non tangential convergence of Poisson-Hermite integrals

We study differentiability conditions on a complex measure $\nu$ at a point $x_0\in\mathbb{R}^d$, in relation with the boundary convergence at that point of the Poisson-type integral $P_t\nu=e^{-t\sqrt L}\nu$, where $L=-\Delta+|x|^2$ is the Hermite operator. In particular, we show that $x_0$ is a Lebesgue point for $\nu$ iff a slightly stronger notion than non-tangential convergence holds for $P_t\nu$ at $x_0$. We also show non-tangential convergence when $x_0$ is a $\sigma$-point of $\nu$, a weaker notion than Lebesgue point, which for $d=1$ coincides with the classical Fatou condition.

math.AP↗

arXiv2023

Pointwise convergence of fractional powers of Hermite type operators

When $L$ is the Hermite or the Ornstein-Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function $f$ so that the fractional power $L^σf(x_0)$ is well-defined at a given point $x_0$. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators $(-Δ+R)^σ$, with $R>0$.

math.AP↗

arXiv2019

Mean value formulas for Ornstein-Uhlenbeck and Hermite temperatures

We obtain explicit mean value formulas for the solutions of the diffusion equations associated with the Ornstein-Uhlenbeck and Hermite operators. From these, we derive various useful properties, such as maximum principles, uniqueness theorems and Harnack-type inequalities.

math.AP↗