arXiv subjects

Estefanía Dalmasso

Publications and source records attributed to Estefanía Dalmasso.

15 recordsLinked to original sources

arXiv2026

A $T1$ criterion for Schrödinger-Calderón-Zygmund operators with exponential decay

We establish the boundedness of exponential Schrödinger-Calderón-Zygmund operators on weighted $BMO_ρ^α(w)$ spaces via a $T1$ criterion, where the weights belong to classes that capture the exponential decay of the operators, and $ρ$ is a critical radius function. Specifically, we prove that the boundedness of such an operator $T$ on $BMO_ρ^α(w)$ is equivalent to a natural oscillation condition on $T1$ over sub-critical balls. The weight classes considered, introduced in connection with $ρ$, include and extend the classical $A_p^ρ$ weights, and are well-adapted to the exponential decay of the kernels. As applications, we derive weighted endpoint estimates for several operators associated to the generalized Schrödinger operator $\mathcal{L}_μ=-Δ+μ$, including Riesz transforms, Laplace transform-type multipliers, maximal operators for the heat and Poisson semigroups, Littlewood-Paley functions and fractional integral operators. When $dμ(x)=V(x)dx$, the results above extend the known endpoint estimates to larger classes of weights.

math.AP↗

arXiv2026

On $m$-order logarithmic Schrödinger operator

In this paper we study the logarithm of order $m$ of the Schrödinger operator $\mathcal L_V$ in $\mathbb R^d$, for certain nonnegative potentials $V$. First, the operator $\log^m\mathcal L_V$, $m\in \mathbb N$, is defined by using the spectral measure associated with the self-adjoint operator $\mathcal L_V$ on a suitable subspace of $L^2(\mathbb R^d)$. Then, the semigroup of operators $\{T_t^V\}_{t>0}$ generated by $\mathcal L_V$ allows us to extend the definition of $\log^m\mathcal L_V$ to a wider class of Lipschitz functions. By using logarithmic operators $\log^m\mathcal L_V$, $m\in \mathbb N$, we prove Taylor expansions for the fractional powers $\mathcal L_V^s$ and $\mathcal L_V^{-s}$ with respect to the order $s\in (0,1)$, where the convergence is understood in $L^p(\mathbb R^d)$, $1<p<\infty$.

math.AP↗

arXiv2026

Logarithmic Schrödinger operators

In this paper we consider the Schrödinger operator $\mathcal L_V= -Δ+ V$ in $\mathbb R^d$ with a non negative potential $V$, and $V\not\equiv 0$. We define the logarithmic Schrödinger operator $\log \mathcal L_V$ proving its main properties. We obtain a pointwise representation of $\log \mathcal L_V$ when $V$ satisfies a reverse Hölder inequality of exponent $q> \frac{d}{2}$ by using the semigroup of operators $\{T_t^V\}_{t>0}$ generated by $\mathcal L_V$. We consider the Lipschitz function space adapted to the Schrödinger setting to solve the initial value problem \[ \begin{cases} \frac{\partial u}{\partial t}=-(\log \mathcal{L}_V)u, & \text{in } \mathbb{R}^n \times (0,\infty), \\ u(x,0)=f(x), & x \in \mathbb{R}^d \end{cases} \] in terms of the fractional integral associated with $\mathcal L_V$.

math.AP↗

arXiv2025

Weighted estimates for Schrödinger-Calderón-Zygmund operators with exponential decay

In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study the boundedness of various operators associated with the generalized Schrödinger operator $-Δ+ μ$, where $μ$ is a nonnegative Radon measure in $\mathbb{R}^d$, for $d\geq 3$.

math.AP↗

arXiv2025

Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators

In this paper we consider fractional Kolmogorov operators defined, in $\mathbb{R}^d$, by \[Λ_κ=(-Δ)^{α/2}+\fracκ{|x|^α} x\cdot \nabla,\] with $α\in (1,2)$, $α<(d+2)/2$ and $κ\in \mathbb{R}$. The operator $Λ_α$ generates a holomorphic semigroup $\{T_t^α\}_{t>0}$ in $L^2(\mathbb{R}^d)$ provided that $κ<κ_c$ where $κ_c$ is a critical coupling constant. We establish $L^p$-boundedness properties for the variation operators $V_ρ\left(\{t^\ell\partial_t^\ell T_t^α\}_{t>0}\right)$ with $ρ> 2$, $\ell\in \mathbb{N}$ and $1\vee \frac{d}β 0})$ is not bounded from $L^p(\mathbb{R}^d)$ to $L^{p,\infty}(\mathbb{R}^d)$ for any $1< p<\infty$.

math.AP↗

arXiv2024

Gaussian $\text{JN}_p$ spaces

In this paper we introduce the John-Nirenberg's type spaces $\text{JN}_p$ associated with the Gaussian measure $dγ(x) = π^{-d/2}e^{-|x|^2}dx$ in $\mathbb{R}^d$ where $1<p<\infty$. We prove a John-Nirenberg inequality for $\text{JN}_p(\mathbb{R}^d,γ)$. We also characterize the predual of $\text{JN}_p(\mathbb{R}^d,γ)$ as a Hardy type space.

math.AP↗

arXiv2024

Endpoint estimates for higher order Gaussian Riesz transforms

We will show that, contrary to the behavior of the higher order Riesz transforms studied so far on the atomic Hardy space $\mathcal{H}^1(\mathbb R^n, γ)$, associated with the Ornstein-Uhlenbeck operator with respect to the $n$-dimensional Gaussian measure $γ$, the new Gaussian Riesz transforms are bounded from $\mathcal{H}^1(\mathbb R^n, γ)$ to $L^1(\mathbb R^n, γ)$, for any order and dimension $n$. We will also prove that the classical Gaussian Riesz transforms of higher order are bounded from an adequate subspace of $\mathcal{H}^1(\mathbb R^n, γ)$ into $L^1(\mathbb R^n, γ)$, extending Bruno's result (J. Fourier Anal. Appl. 25, 4 (2019), 1609--1631) for the first order case.

math.CA↗

arXiv2022

Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),γ_α)$ to $L^1((0,\infty),γ_α)$ and also from $L^\infty((0,\infty),γ_α)$ to $\BMO((0,\infty),γ_α)$, with respect to the probability measure $dγ_α(x)=\frac{2}{Γ(α+1)} x^{2α+1} e^{-x^2} dx$ on $(0,\infty)$ when ${α>-\frac12}$. We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting.

math.CA↗

arXiv2022

Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions

In this paper we introduce the atomic Hardy space $\mathcal{H}^1((0,\infty),γ_α)$ associated with the non-doubling probability measure $dγ_α(x)=\frac{2x^{2α+1}}{Γ(α+1)}e^{-x^2}dx$ on $(0,\infty)$, for ${α>-\frac12}$. We obtain characterizations of $\mathcal{H}^1((0,\infty),γ_α)$ by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from $\mathcal{H}^1((0,\infty),γ_α)$ into $L^1((0,\infty),γ_α)$.

math.AP↗

arXiv2022

Harmonic analysis operators associated with Laguerre polynomial expansions on variable Lebesgue spaces

In this paper we give sufficient conditions on a measurable function $p:(0,\infty)^n\rightarrow [1,\infty)$ in order that harmonic analysis operators (maximal operators, Riesz transforms, Littlewood--Paley functions and multipliers) associated with $α$-Laguerre polynomial expansions are bounded on the variable Lebesgue space $L^{p(\cdot)} ((0,\infty)^n, μ_α)$, where $dμ_α(x)=2^n\prod_{j=1}^n \frac{x_j^{2α_j+1} e^{-x_j^2}}{Γ(α_j+1)} dx$, being $α=(α_1, \dots, α_n)\in [0,\infty)^n$ and $x=(x_1,\dots,x_n)\in (0,\infty)^n$.

math.CA↗

arXiv2021

New Gaussian Riesz transforms on variable Lebesgue spaces

We give sufficient conditions on the exponent $p: \mathbb R^d\rightarrow [1,\infty)$ for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces $L^{p(\cdot)}(\mathbb R^d, γ_d)$, as well as of the new higher order Riesz transforms associated with the Ornstein-Uhlenbeck semigroup, which are the natural extensions of the supplementary first order Gaussian Riesz transforms defined by A. Nowak and K. Stempak in \cite{nowakstempak}.

math.AP↗

arXiv2019

$L^p$--boundedness of Stein's square functions associated to Fourier--Bessel expansions

In this paper we prove $L^p$ estimates for Stein's square functions associated to Fourier-Bessel expansions. Furthermore we prove transference results for square functions from Fourier-Bessel series to Hankel transforms. Actually, these are transference results for vector-valued multipliers from discrete to continuous in the Bessel setting. As a consequence, we deduce the sharpness of the range of $p$ for the $L^p$-boundedness of Fourier-Bessel Stein's square functions from the corresponding property for Hankel-Stein square functions. Finally, we deduce $L^p$ estimates for Fourier-Bessel multipliers from that ones we have got for our Stein square functions.

math.CA↗

arXiv2018

Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings

In this article we prove dimension free $L^p$-boundedness of Riesz transforms associated with a Bessel diferential operator. We obtain explicit estimates of the $L^p$-norms for the Bessel-Riesz transforms in terms of p, establishing a linear behaviour with respect to p. We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator.

math.CA↗

arXiv2017

Local Hardy spaces with variable exponents associated to non-negative self-adjoint operators satisfying Gaussian estimates

In this paper we introduce variable exponent local Hardy spaces associated with a non-negative self-adjoint operator L. We define them by using an area square integral involving the heat semigroup associated to L. A molecular characterization is established and as an aplication of the molecular characterization we prove that our local Hardy space coincides with the (global) variable exponent Hardy space associated to L, provided that 0 does not belong to the spectrum of L. Also, we show that it coincides with the global variable exponent Hardy space associated to L+I.

math.CA↗

arXiv2017

The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander's type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of $p$.

math.AP↗