Browsing by Subject "Poisson integral"

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    Lebesgue points of measures and non tangential convergence of Poisson-Hermite integrals
    (Springer, 2025-05-22) Flores, Guillermo; Garrigós Aniorte, Gustavo Adolfo; Viviani, Beatriz; Matemáticas
    We study differentiability conditions on a complex measure \nu at a point x_0, in relation with the boundary convergence at that point of the Poisson-type integral P_t\nu = exp(-t\sqrt L) \nu , where L 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. 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