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+34 946 567 842
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+34 946 567 842
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lroncal@bcamath.org
Information of interest
- Orcid: 0000-0003-0852-3677
Ikerbasque Research and Ramón y Cajal Fellow.
My research concerns problems from Harmonic Analysis and Partial Differential Equations.
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Weak-type maximal function estimates on the infinite-dimensional torus
Kosz, D.
; Rey, G.; Roncal, L. (2023-07)
We prove necessary and sufficient conditions for the weak- $L^p$ boundedness, for $p\in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality ...
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ON (GLOBAL) UNIQUE CONTINUATION PROPERTIES OF THE FRACTIONAL DISCRETE LAPLACIAN
Fernández-Bertolin, A.; Roncal, L.; Rüland, A. (2023)
We study various qualitative and quantitative (global) unique continuation prop- erties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of ...
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ENDPOINT ESTIMATES AND OPTIMALITY FOR THE GENERALIZED SPHERICAL MAXIMAL OPERATOR ON RADIAL FUNCTIONS
Nowak, A.; Roncal, L.; Szarek, T.Z. (2023)
We find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions Mtα,β to be bounded on power weighted Lebesgue spaces. Moreover, we also obtain the corresponding ...
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Pointwise localization and sharp weighted bounds for Rubio de Francia square functions
Di Plinio, F.; Florez, M.; Parissis, I.; Roncal, L. (2023)
Let 𝐻𝜔 𝑓 be the Fourier restriction of 𝑓 ∈ 𝐿2 (R) to an interval 𝜔 ⊂ R. If Ω is an arbitrary collection of pairwise disjoint intervals, the square function of {𝐻𝜔 𝑓 : 𝜔 ∈ Ω} is termed the Rubio de Francia square ...
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Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group
Fanelli, L.; Roncal, L. (2022-11-04)
We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and Littlewood--Paley ...
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The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
Kumar, S.; Ponce Vanegas, F.; Roncal, L.; Vega, L. (2022)
We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ...
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MAXIMAL OPERATORS ON THE INFINITE-DIMENSIONAL TORUS
Kosz, D.; Martinez-Perales, J.C.; Paternostro, V.; Rela, E.; Roncal, L. (2022)
We study maximal operators related to bases on the infinite- dimensional torus Tω. For the normalized Haar measure dx on Tω it is known that MR0, the maximal operator associated with the dyadic basis R0, is of weak type ...
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HARDY TYPE INEQUALITIES FOR THE FRACTIONAL RELATIVISTIC OPERATOR
Roncal, L. (2022)
We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of ...
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Singular integrals along variable codimension one subspaces
Di Plinio, F.; Parissis, I.; Roncal, L. (2022)
This article deals with maximal operators on R𝑛 formed by taking arbitrary rota- tions of tensor products of a 𝑑-dimensional Hörmander–Mihlin multiplier with the identity in 𝑛 − 𝑑 coordinates, in the particular ...
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Discrete Carleman estimates and three balls inequalities
Fernández-Bertolin, A.; Roncal, L.; Rüland, A.; Stan, D. (2021-10-16)
We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the ...
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Bilinear Spherical Maximal Functions of Product Type
Roncal, L.; Shrivastava, S.; Shuin, K. (2021-08-12)
In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ...
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Variation bounds for spherical averages
Beltran, D.; Oberlin, R.; Roncal, L.; Stovall, B.; Seeger, A. (2021-06-22)
We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates
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Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups
Roncal, L.; Thangavelu, S. (2021-03-10)
Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 4238--4294. They concern ...
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Cp ESTIMATES FOR ROUGH HOMOGENEOUS SINGULAR INTEGRALS AND SPARSE FORMS
Canto, J.; Li, K.; Roncal, L.; Tapiola, O. (2021)
We consider Coifman–Fefferman inequalities for rough homogeneous singular integrals TΩ and Cp weights. It was recently shown in [33] that ∥TΩ∥Lp(w) ≤ Cp,T,w∥Mf∥Lp(w) for every 0 < p < ∞ and every w ∈ A∞. Our first goal ...
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A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus
Fernández, E.; Roncal, L. (2020-02-13)
In this note we will show a Calder\'on--Zygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting ...
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Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
Ciaurri Ó.; Nowak, A.; Roncal, L. (2020)
We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ...
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DIRECTIONAL SQUARE FUNCTIONS
Accomazzo, N.; Di Plinio, F.; Hagelstein, P.; Parissis, I.; Roncal, L. (2020)
QuantitativeformulationsofFefferman’scounterexamplefortheballmultiplierare naturally linked to square function estimates for conical and directional multipliers. In this ar- ticle we develop a novel framework for these ...
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Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function
Garg, R.; Roncal, L.; Shrivastava, S. (2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ...
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Carleman type inequalities for fractional relativistic operators
Stan, D.; Roncal, L.; Vega, L. (2019-09-22)
In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ...
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On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
Boggarapu, P.; Roncal, L.; Thangavelu, S. (2019-09)
We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ...
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On the absolute divergence of Fourier series in the infinite dimensional torus
Fernández, E.; Roncal, L. (2019-03-22)
In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ...
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$A_1$ theory of weights for rough homogeneous singular integrals and commutators
Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2019)
Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
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Weighted norm inequalities for rough singular integral operators
Li, K.; Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2018-08-17)
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...
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Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
Lizama, C.; Roncal, L. (2018)
We study the equations $ \partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $ \partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ...
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Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator
Ciaurri Ó.; Roncal, L.; Thangavelu, S. (2018)
We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...
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Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
Ciaurri Ó.; Nowak, A.; Roncal, L. (2018)
We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ...
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Vector-valued extensions for fractional integrals of Laguerre expansions
Ciaurri Ó.; Roncal, L. (2018)
We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ...
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Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
Ciaurri Ó.; Roncal, L.; Stinga, P.R.; Torrea, J.L.; Varona, J.L. (2018)
The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ...
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Quantitative weighted estimates for rough homogeneous singular integrals
Hytönen, T.P.; Roncal, L.; Tapiola, O. (2017-03-11)
We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
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Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions
Boggarapu, P.; Roncal, L.; Thangavelu, S. (2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
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$A_1$ theory of weights for rough homogeneous singular integrals and commutators
Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2016-07-01)
Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ...
