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Beatriz Viviani

Publications and source records attributed to Beatriz Viviani.

6 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 $ν$ at a point $x_0\in\mathbb{R}^d$, in relation with the boundary convergence at that point of the Poisson-type integral $P_tν=e^{-t\sqrt L}ν$, where $L=-Δ+|x|^2$ is the Hermite operator. In particular, we show that $x_0$ is a Lebesgue point for $ν$ iff a slightly stronger notion than non-tangential convergence holds for $P_tν$ at $x_0$. We also show non-tangential convergence when $x_0$ is a $σ$-point of $ν$, 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↗
arXiv2015

A.e. convergence and 2-weight inequalities for Poisson-Laguerre semigroups

We find optimal decay estimates for the Poisson kernels associated with various Laguerre-type operators L. From these, we solve two problems about the Poisson semigroup $e^{-t\sqrt{L}}$. First, we find the largest space of initial data $f$ so that $e^{-t\sqrt{L}}f(x)\to f(x)$ at a.e. $x$. Secondly, we characterize the largest class of weights $w$ which admit 2-weight inequalities of the form $\|\sup_{0<t\leq t_0}|e^{-t\sqrt{L}}f|\,\|_{L^p(v)}\lesssim \|f\|_{L^p(w)}$, for some other weight $v$.

math.AP↗
arXiv2015

Interior Lp-estimates for elliptic and parabolic Schrödinger type operators and local Ap-weights

Let Omega be a non-empty open proper and connected subset of R^n. Consider p elliptic Schrödinger type operator L_{E}u=A_{E}u+V in Omega, and the linear parabolic operator L_{P}u=A_{P}u+Vu in Omega x (0,T), where the coefficients of A_{E} and A_{P} are in VMO and the potential V satisfies a reverse-Hölder condition. The aim of this paper is to obtain a priori estimates for the operators L_{E} and L_{P} in weighted Sobolev spaces involving the distance to the boundary and weights in a local-A class.

math.AP↗
arXiv2009

Wavelet expansions for weighted, vector-valued BMO functions

We introduce a scale of weighted Carleson norms, which depend on an integrability parameter p, where p=2 corresponds to the classical Carleson measure condition. Relations between the weighed BMO norm of a vector-valued function f:R->X, and the Carleson norm of the sequence of its wavelet coefficients, are established. These extend the results of Harboure-Salinas-Viviani, also in the scalar-valued case when p is not 2.

math.FA↗