IMAL Preprints
Esta serie reúne las ediciones previas de trabajos de investigación que serán sometidos a referato en revistas de la disciplina.
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A continuación se listan los IMAL Preprints clasificados por año de edición.
2024
Mauricio Ramseyer – Oscar Salinas – Juan Sotto Ríos – Marisa Toschi
Abstract
Let be a proper open subset of
We give sufficient conditions about local weights for the two-weight norm inequality for the local fractional maximal and the local fractional integral operator acting on weighted Lebesgue spaces. By using the technique of
sparse operators we obtained improved results taking into account the proposed hypotheses. As applications we obtain a priori estimate for solutions of
in
, acting in weighted Sobolev spaces involving the distance to the boundary and different local weights. In the context of Schödinger type operators we prove as another application the boundedness of the Riesz potential
, for
,
and
be a Radon measure on
. Some illuminating examples are set out at the end of the article.
Estefanía Dalmasso – Gabriela R. Lezama – Marisa Toschi
Abstract
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 where
is a nonnegative Radon measure in
for
.
Hugo Aimar – Ignacio Gómez Vargas – Ivana Gómez – Francisco Javier Martín-Reyes
Abstract
In this work, we introduce the geometric concept of one-sided weakly porous sets in the real line and show that a set satisfies
for some
if and only if
is right-sided weakly porous. Furthermore, we find that the property of being both left-sided and right-sided weakly porous is equivalent to the recent weakly porous condition discussed in the bibliography, which, in turn, was previously found to be intimately related to the usual class of Muckenhoupt weights
.
Jorge J. Betancor – Estefanía Dalmasso – Pablo Quijano
Abstract
In this paper we introduce the John-Nirenberg’s type spaces associated with the Gaussian measure
in
where
. We prove a John-Nirenberg inequality for
. We also characterize the predual of
as a Hardy type space.
Hugo Aimar – Ignacio Gómez Vargas – Ivana Gómez
Abstract
In this work we characterize the sets for which there is some
such that the function
belongs to the Muckenhoupt class
where
is a space of homogeneous type, extending a recent result obtained by Carlos Mudarra in metric spaces endowed with doubling measures. In particular, generalizations of the notions of weakly porous sets and doubling of the maximal hole function are given and it is shown that these concepts have a natural connection with the
condition of some negative power of its distance function. The proof presented here is based on Whitney-type covering lemmas built on balls of a particular quasi-distance equivalent to the initial quasi-distance
and provided by Roberto Macías and Carlos Segovia in “A well-behaved quasi-distance for spaces of homogeneous type”, Trabajos de Matemática 32, Instituto Argentino de Matemática, 1981, 1-18.
Federico Campos, Oscar Salinas, Beatriz Viviani
Abstract
In a bounded connected open set we obtain an interior a priori estimate for solutions of certain elliptic differential equations, with norms in a
space related to weights in a “local” Muckenhoupt’s class.
Hugo Aimar – Carlos Exequiel Arias – Ivana Gómez
Abstract
In this paper we use the neighborhood topology generated by affinities between pairs of points in a set, in orden to explore the underlying dynamics of connectivity by thresholding of the affinity. We apply the method to the connectivity provided by the public transport system in Buenos Aires.
Hugo Aimar – Aníbal Chicco Ruiz – Ivana Gómez
Abstract
In this article we aim to obtain the Fisher Riemann geodesics for non parametric families of probability densities as a weak limit of the parametric case with increasing number of parameters.
2023
Bruno Bongioanni – Marisa Toschi – Bruno Urrutia
Abstract
In this work we obtain boundedness results for the fractional integral operator of the the bi-harmonic Schrödinger operator on weighted Lebesgue and BMO type spaces in with
. The techniques are based on some new estimates involving the kernel of the heat semigroup.
Jorge J. Betancor – Estefanía Dalmasso – Pablo Quijano
Abstract
We represent by the semigroup generated by
, where
is a Hardy operator on a half space. The operator
includes a fractional Laplacian and it is defined by
We prove that, for every , the
-variation operator
is bounded on
for each
and
, being
the Muckenhoupt
-class of weights on
.
Nadia Barreiro – Pablo Bolcatto – Tzipe Govezensky – Cecilia Ventura
Matías Nuñez – Rafael Ángel Barrio
Abstract
En los últimos años, el COVID-19 ha avanzado por todo el mundo generado millones de contagios y fallecimientos. Sin embargo, existen múltiples factores que han modificado significativamente su evolución. Entre ellos pueden enumerarse, la aparición de variantes, el desarrollo de vacunas y las medidas tomadas por cada gobierno.
Con el objetivo de comprender la incidencia de dichos factores, en este trabajo se muestra un modelo epidemiológico geo-estocástico que, integrando parámetros epidemiológicos, demográficos y sociales, permite estudiar la evolución de la pandemia en una región o un país. Este utiliza un sistema de ecuaciones discretas demoradas en el tiempo basado
en un modelo compartimental SEIR modificado para incluir tanto las nuevas variantes como la vacunación. El modelo se aplicó tanto en regiones ficticias como en países y permitió reproducir el comportamiento real de la pandemia y estudiar diferentes escenarios de evolución.
Dalma Bilbao, Hugo Aimar, Diego Mateos
[Artículo completo]: Versión 2 del IMAL Preprint 2022-0061
Abstract
The rapid growth of large datasets has led to a demand for novel approaches to extract valuable insights from intricate information. Graph theory provides a natural framework to model these relationships, but
standard graphs may not capture the complex interdependence between components. Hypergraphs, are a powerful extension of graphs that can represent higher-order relationships in the data. In this paper, we propose a novel approach to studying the metric structure of a dataset using hypergraph theory and a filtration method. Our method involves building a set of hypergraphs based on a variable distance parameter, enabling us to infer qualitative and quantitative information about the data structure. We apply our method to various sets of points, dynamical systems, signal models, and real electrophysiological data.Our results show that the proposed method can effectively differentiate between different data sets, demonstrating its potential utility in a range of scientific applications
Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano
[Artículo completo]
Abstract
In this paper we introduce spaces of -type related to Laguerre polynomial expansions. We consider the probability measure on
defined by
with
. For every
, the space
consists of all those measurable functions defined on
having bounded lower oscillation with respect to
over an admissible family
of intervals in
. The space
is a subspace of the space
of bounded mean oscillation functions with respect to
and
. The natural
-local centered maximal function defined by
is bounded from
into
. We prove that the maximal operator, the
-variation and the oscillation operators associated with local truncations of the Riesz transforms in the Laguerre setting are bounded from
into
. Also, we obtain a similar result for the maximal operator of local truncations for spectral Laplace transform type multipliers.
2022
Federico Campos, Oscar Salinas, Beatriz Viviani
[Artículo completo]
Abstract
In a general geometric setting, we prove different characterizations of a local version of Muckenhoupt weights. As an application, we obtain conclusions about the relationship between this class and the one-weight boundedness of local singular integrals from
to
Dalma Bilbao, Hugo Aimar, Diego M. Mateos
[Artículo completo]: versión actualizada disponible en IMAL Preprint 2023-0064
Abstract
In this paper we aim to use different metrics in the Euclidean space and Sobolev type metrics in function spaces in order to produce reliable parameters for the differentiation of point distributions and dynamical systems. The main tool is the analysis of the geometrical evolution of the hypergraphs generated by the growth of the radial parameters for a choice of an appropriate metric in the space containing the data points. Once this geometric dynamics is obtained we use Lebesque and Sobolev type norms in order to compare the basic geometric signals obtained.
Angel Ciarbonetti, Sergio Idelsohn, Ruben D. Spies
[Artículo completo]
Abstract
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in , from the knowledge of the state over the whole domain. We develop a method based on a variational approach leading to an optimality equation which is then projected into a finite dimensional space. Discretization yields a linear although severely ill-posed equation which is then regularized via appropriate ad-hoc penalizers resulting a in a generalized Tikhonov-Phillips functional.
No smoothness assumptions are imposed on the conductivity. Numerical examples for the case in which the conductivity can take only two prescribed values (a two-materials case) show that the approach is able to produce very good reconstructions of the exact solution.
Hugo Aimar, Federico Morana
[Artículo completo]
Abstract
In this brief note we aim to provide, through a well known class
of singular densities in harmonic analysis, a simple approach to the fact that the homogeneity of the universe on scales of the order of a hundred millions light years is completely compatible with the fine-scale condensation of matter and energy. We give precise and quantitative definitions of homogeneity and isotropy on large scales. Then we show that Muckenhoupt densities have the ingredients required to a model for the large-scale homogeneity and the fine-scale condensation of the universe. In particular, these densities can take
locally infinitely large values (black holes) and at once, in the large scales they are independent of the location. We also show some locally singular densities satisfying the large scale isotropy property.
Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto
[Artículo completo]
Abstract
In this paper we give a criterion to prove boundedness results for several operators from to
and also from
to
, with respect to the probability measure
on
when
. 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.
Hugo Aimar, Carlos Exequiel Arias, Ivana Gómez
[Artículo completo]
Abstract
We obtain a necessary and sufficient condition on the Haar coefficients of a real function defined on
for the Lipschitz
regularity of
with respect to the ultrametric
where
is the family of all dyadic intervals in
and
is positive. Precisely,
if and only if
, for some constant
, every
and every
Here, as usual
and
.
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Publicaciones del IMAL: IMAL Preprints
ISSN 2451-7100
Instituto de Matemática Aplicada del Litoral «Dra. Eleonor Harboure»
CONICET-UNL
Colectora Ruta Nac. 168 – km 472, Paraje El Pozo
3000 Santa Fe, Argentina
Tel: (+54)342-4511370, Int. 4001/3
Fax: (+54)342-4510368
E-mail: imal@santafe-conicet.gov.ar
Directora: Dra. Estefanía Dalmasso – edalmasso@santafe-conicet.gov.ar
Comité Editorial: Dr. Hugo Aimar, Dr. Oscar Salinas, Dr. Rubén Spies, Dra. Beatriz Viviani
Colaboradores: Dr. Mauricio Ramseyer, Lic. Marcela Porta