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+34 946 567 842
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+34 946 567 843
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lroncal@bcamath.org
Information of interest
- Orcid: 0000-0003-0852-3677
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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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$A_1$ 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 ...
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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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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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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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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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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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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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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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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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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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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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Maximal operators on the infinite-dimensional torus
Roncal, Luz; Kosz, D.; Martínez-Perales, J.; Paternostro, V.; Rela, E.; Roncal, L. (2022-03-31)
We study maximal operators related to bases on the infinite-dimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ...
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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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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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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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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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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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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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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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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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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 ...