Laura Prat

activity

20042026

most cited

L^{2}

-boundedness of gradients of single layer potentials and uniform rectifiability

4 citations · 4 across the 12 of their papers we have counts for

collaborators

16 papers

physics.chem-ph2026

Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation

Vincenzo Barone

Anharmonic intensities reveal vibrational coupling that band positions alone cannot determine. We derive explicit second-order infrared transition moments in curvilinear normal coo…

math.AP2026

$L^{2}$ -boundedness of the $n$ -th Calderón commutator on Lipschitz graphs

Joan Hernández, Joan Mateu, Laura Prat

This paper investigates the asymptotic behavior of the norm, as a bounded operator in $L^{2} (R)$ , of the $n$ -th Calderón commutator $T_{A, n}$ on the graph of a Lipschitz fun…

math.AP2024

On fractional parabolic $BMO$ and $Lip_{α}$ caloric capacities

Joan Hernández, Joan Mateu, Laura Prat

In the present paper we characterize the removable sets for solutions of the fractional heat equation satisfying some parabolic $BMO$ or $Lip_{α}$ normalization conditi…

math.AP2024

On the semi-additivity of the $1/2$ -symmetric caloric capacity

Joan Hernández, Joan Mateu, Laura Prat

In this paper we study properties of a variant of the $1/2$ -caloric capacity, called $1/2$ -symmetric caloric capacity. The latter is associated simultaneously with the $1/2$ -fracti…

math.AP2022

Removable singularities for solutions of the fractional Heat Equation in time varying domains

Joan Mateu, Laura Prat

In this paper we study removable singularities for solutions of the fractional heat equation in time varying domains. We introduce associated capacities and we study some of its me…

math.CA2020

Removable singularities for Lipschitz caloric functions in time varying domains

Joan Mateu, Laura Prat, Xavier Tolsa

In this paper we study removable singularities for regular $(1, 1/2)$ -Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric…

math.CA2019

$L^{2}$ -bounded singular integrals on a purely unrectifiable set in $R^{d}$

Joan Mateu, Laura Prat

We construct an example of a purely unrectifiable measure $μ$ in $R^{d}$ for which the singular integrals associated to the kernels $\displaystyle{K(x)=\frac{P_{2k+1}(x)}{|x…

math.CA2018★ 4 cited

$L^{2}$ -boundedness of gradients of single layer potentials and uniform rectifiability

Laura Prat, Carmelo Puliatti, Xavier Tolsa

Let $A (\cdot)$ be an $(n + 1) \times (n + 1)$ uniformly elliptic matrix with Hölder continuous real coefficients and let $E_{A} (x, y)$ be the fundamental solution of the PDE $\mat…

math.FA2015

Non-existence of reflectionless measures for the s-Riesz transform when 0<s<1

Laura Prat, Xavier Tolsa

A measure $μ$ on $R^{d}$ is called reflectionless for the $s$ -Riesz transform if the singular integral $R^{s} μ (x) = \int \frac{y - x}{∣ y - x ∣ ^{s + 1}} d μ (y)$ is constant on the suppo…

math.CA2014

Square functions of fractional homogeneity and Wolff potentials

Vasileios Chousionis, Laura Prat, Xavier Tolsa

In this paper it is shown that for anymeasure $μ$ in $R^{d}$ and for a non-integer $0 < s < d$ , the Wolff energy $\displaystyle{\iint_0^\infty(\frac{μ(B(x,r))}{r^s})^2\,\frac{dr…

math.CA2014

Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability

Vasilis Chousionis, Laura Prat

We consider the Calderón-Zygmund kernels $K_{α, n} (x) = (x_{i}^{2 n - 1} /∣ x ∣^{2 n - 1 + α})_{i = 1}^{d}$ in $R^{n}$ for $0 < α \leq 1$ and $n \in N$ . We show that, on the plane, for $0<…

math.CA2011

Capacities associated with Calderón-Zygmund kernels

Vasilis Chousionis, Joan Mateu, Laura Prat +1

Analytic capacity is associated with the Cauchy kernel $1/ z$ and the $L^{\infty}$ -norm. For $n \in N$ , one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x…

math.CA2011

Calderón-Zygmund kernels and rectifiability in the plane

Vasilis Chousionis, Joan Mateu, Laura Prat +1

Let $E \subset \C$ be a Borel set with finite length, that is, $0 < H^{1} (E) < \infty$ . By a theorem of David and Léger, the $L^{2} (H^{1} ⌊ E)$ -boundedness of the…

math.CA2010

On the semiadditivity of the capacities associated with signed vector valued Riesz kernels

Laura Prat

The aim of this paper is to show the semiadditivity of the capacities associated to the signed vector valued Riesz kernels of homogeneity $- α$ in $R^{n}$ , with $0 < α < n$ .

math.CA2010

Capacities associated with scalar signed Riesz kernels, and analytic capacity

Joan Mateu, Laura Prat, Joan Verdera

The real and imaginari parts of the Cauchy kernel in the plane are scalar Riesz kernels of homogeneity -1. One can associate with each of them a natural notion of capacity related…

math.CA2004

The capacity associated to signed Riesz kernels, and Wolff potentials

Joan Mateu, Laura Prat, Joan Verdera

There is a natural capacity associated to any vector valued Riesz kernel of a given homogeneity. If we are in the plane and the kernel is the Cauchy kernel, then this capacity is a…

Cartesian and Curvilinear Anharmonic Frequencies and Intensities: Perturb-then-Diagonalize Polyad Transport and Adiabatic Discrete-Variable Representation

L2-boundedness of the n-th Calderón commutator on Lipschitz graphs

On fractional parabolic BMO and Lipα​ caloric capacities

On the semi-additivity of the 1/2-symmetric caloric capacity

Removable singularities for solutions of the fractional Heat Equation in time varying domains

Removable singularities for Lipschitz caloric functions in time varying domains

L2-bounded singular integrals on a purely unrectifiable set in Rd

L2-boundedness of gradients of single layer potentials and uniform rectifiability

Non-existence of reflectionless measures for the s-Riesz transform when 0<s<1

Square functions of fractional homogeneity and Wolff potentials

Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability

Capacities associated with Calderón-Zygmund kernels

Calderón-Zygmund kernels and rectifiability in the plane

On the semiadditivity of the capacities associated with signed vector valued Riesz kernels

Capacities associated with scalar signed Riesz kernels, and analytic capacity

The capacity associated to signed Riesz kernels, and Wolff potentials

$L^{2}$ -boundedness of the $n$ -th Calderón commutator on Lipschitz graphs

On fractional parabolic $BMO$ and $Lip_{α}$ caloric capacities

On the semi-additivity of the $1/2$ -symmetric caloric capacity

$L^{2}$ -bounded singular integrals on a purely unrectifiable set in $R^{d}$

$L^{2}$ -boundedness of gradients of single layer potentials and uniform rectifiability