Papers by Alvaro Corvalán
Recientemente se ha observado que para un peso w la desigualdad puntual para operadores de Hardy-... more Recientemente se ha observado que para un peso w la desigualdad puntual para operadores de Hardy-Littlewood Mf (x)^p ≤ C · M_w (| f |^p| ) (x), que es consecuencia del tipo débil (p, p) respecto de un peso w en realidad es equivalente a la acotación débil (p, p). Aquí proporcionamos una demostración nueva y elemental de dicha equivalencia que, a diferencia de las demostraciones existentes, no requiere apoyarse en resultados de cubrimientos. The inequality Mf (x)p C Mw (j f jp) (x), for a weight function w, is a consequence of the weak type (p; p) for the Hardy-Littlewood maximal operator from Lp (w). A recent result shows that the inequality also implies the weak type(p; p) so, in fact, both conditions are equivalent. Here we give a new an elementary proof of the equivalence that, unlike existing demonstrations, it requires no covering properties
Los criterios suficientes usuales que garantizan la estabilidad de un sistema diferencial lineal ... more Los criterios suficientes usuales que garantizan la estabilidad de un sistema diferencial lineal impulsivo requieren condiciones muy particulares sobre las matrices que definen el sistema, que raramente se satisfacen al usar estos modelos para problemas aplicados reales. Aquí presentamos un criterio sencillo que no requiere que las matrices tengan una forma especial, o que tengan alguna relación particular entre ellas. The usual sufficient criteria to ensure the stability of an impulsive linear differential system require very particular conditions on the matrices that define the system, which are rarely satisfied when using these models to realistic applied problems. Here we present a simple approach that does require nor a special form for the matrices neither a particular relationship between them.
arXiv (Cornell University), Oct 24, 2017
The purpose of this paper is to give some characterizations of the weight functions w such that M... more The purpose of this paper is to give some characterizations of the weight functions w such that M w ∈ A∞. We show that for those weights to be in A∞ ensures to be in A1. We give a criterion in terms of the local maximal functions m λ and we present a pair of applications, one of them similar to the Coifman-Rochberg characterization of A1 but using functions of the form f # δ and (m λ u) δ instead of (M f) δ .
Laboratornaya sluzhba, 2017
Real Analysis Exchange, 2014
The purpose of this paper is to find necessary and sufficient conditions on the weight w for the ... more The purpose of this paper is to find necessary and sufficient conditions on the weight w for the weak type (p, p) with 1 ≤ p < +∞ and for the strong type (p, p) with 1 < p < +∞ respect to a measure wdx of the vector-valued one-sided maximal operator M + g r .
The purpose of this paper is to give some characterizations of the weight functions w such that M... more The purpose of this paper is to give some characterizations of the weight functions w such that Mw is in A_∞. We show that for those weights to be in A_∞ ensures to be in A_1. We give a criterion in terms of the local maximal functions m_λ and we present a pair of applications, among them someone similar to the Coifman-Rochberg characterization of A_1 but using functions of the form (f^#)^δ and (m_λu)^δ instead of (Mf)^δ.
Real Analysis Exchange
The purpose of this paper is to give some characterizations of the weight functions w such that M... more The purpose of this paper is to give some characterizations of the weight functions w such that M w ∈ A∞. We show that for those weights to be in A∞ ensures to be in A1. We give a criterion in terms of the local maximal functions m λ and we present a pair of applications, one of them similar to the Coifman-Rochberg characterization of A1 but using functions of the form f # δ and (m λ u) δ instead of (M f) δ .
The usual sufficient criteria to ensure the stability of an impulsive linear differential system ... more The usual sufficient criteria to ensure the stability of an impulsive linear differential system require very particular conditions on the matrices that define the system, which are rarely satisfied when using these models to realistic applied problems. Here we present a simple approach that does require nor a special form for the matrices neither a particular relationship between them.
arXiv: Functional Analysis, 2019
Extending results in \cite{M} and \cite{MM} we characterize the classical classes of weights that... more Extending results in \cite{M} and \cite{MM} we characterize the classical classes of weights that satisfy reverse Holder inequalities in terms of indices of suitable families of $K-$functionals of the weights. In particular, we introduce a Samko type of index (cf. \cite{kara}) for families of functions, that is based on quasi-monotonicity, and use it to provide an index characterization of the $RH_{p}$ classes, as well as the limiting class $RH=$ $RH_{LLogL}=$. $\bigcup\limits_{p>1}RH_{p}$ (cf. \cite{BMR}),\ which in the abstract case involves extrapolation spaces. Reverse Holder inequalities associated to $L(p,q)$ norms, and non-doubling measures are also treated.
Extending results in [50] and [49] we characterize the classical classes of weights that satisfy ... more Extending results in [50] and [49] we characterize the classical classes of weights that satisfy reverse Hölder inequalities in terms of indices of suitable families of K−functionals of the weights. In particular, we introduce a Samko type of index (cf. [41]) for families of functions, that is based on quasi-monotonicity, and use it to provide an index characterization of the RHp classes, as well as the limiting class RH = RHLLogL =. ⋃ p>1 RHp (cf. [8]), which in the abstract case involves extrapolation spaces. Reverse Hölder inequalities associated to L(p, q) norms, and non-doubling measures are also treated.
The inequality Mf (x)p C Mw (j f jp) (x), for a weight function w, is a consequence of the weak t... more The inequality Mf (x)p C Mw (j f jp) (x), for a weight function w, is a consequence of the weak type (p; p) for the Hardy-Littlewood maximal operator from Lp (w). A recent result shows that the inequality also implies the weak type (p; p) so, in fact, both conditions are equivalent. Here we give a new an elementary proof of the equivalence that, unlike existing demonstrations, it requires no covering properties.
The purpose of this paper is to find necessary conditions and sufficient conditions on the pair o... more The purpose of this paper is to find necessary conditions and sufficient conditions on the pair of weights (u,v) for the boundedness of the one-sided operators N_{α,β}^{+} from L_{dec}^{p}(v) into L^{q}(u) in the case 1<p≤q<+∞.
The purpose of this paper is to find necessary conditions and sufficient conditions on the pair o... more The purpose of this paper is to find necessary conditions and sufficient conditions on the pair of weights (u,v) for the boundedness of the one-sided operators N_{α,β}^{+} from L_{dec}^{p}(v) into L^{q}(u) in the case 1<p≤q<+∞.
We consider the problem of obtaining information about the recognition of logical inconsistencies... more We consider the problem of obtaining information about the recognition of logical inconsistencies with already imprinted patterns of a subnetwork of a neural network, both cerebral and artificially designed, by means of the measurement of the event related potentials (ERP). One of the subsequent aims, it is the detection of logical inconsistencies of the speech, not purely semantic, but of the recognition of not coherent phrases with a story line. The possibility of the use, with this goal, of ERP obtained of superficially located electrodes on the scalp would be interesting: relevant conclusions would be obtained from a non-invasive method and by means of equipment that is relatively economic, easily transportable and installable. The alternative that we propose is the utilization of Kalman type filters (with necessary modifications). The idea is to deal with the evoked response as a not accessible variable, with a relation (non linear, but locally linealizable) respect to the meas...
The purpose of this paper is to find necessary and sufficient conditions on the weight w for the ... more The purpose of this paper is to find necessary and sufficient conditions on the weight w for the weak type (p,p) with 1≤p<+∞ and for the strong type (p,p) with 1<p<+∞ respect to a measure wdx of the vector-valued one-sided maximal operator (M_{g}+)_{r}.
Revista de Matemática: Teoría y Aplicaciones, 2011
Consideramos el problema de la obtención de información acerca del reconocimiento de incongruenci... more Consideramos el problema de la obtención de información acerca del reconocimiento de incongruencias con patrones lógicos ya impresos de una subred de una red neuronal, ya sea cerebral, o diseñada artificialmente, mediante la medición de los potenciales evocados (PE) cerebrales. Uno de los objetivos ulteriores, es la detección de inconsistencias lógicas del discurso, no puramente semánticas, sino del reconocimiento de frases no coherentes con una línea de relato. La posibilidad del uso, con este fin, de PE obtenidos de electrodos ubicados superficialmente sobre el cuero cabelludo sería interesante: serían obtenidas conclusiones relevantes a partir de un método no-invasivo y mediante un equipamiento que es relativamente económico, de fácil transporte e instalación. La alternativa que proponemos es la utilización de filtros tipo Kalman (con necesarias modificaciones). La idea es tratar a la respuesta evocada como una variable no accesible, con una relación (no lineal, pero localmente linealizable) respecto de la variable mensurable. Estudiamos, como ejemplo guía, la evolución de una variable que mide, en una red neuronal de atractores tipo Hopfield, el ajuste entre el estado de una subred asociada al reconocimiento de ciertos patrones, luego de una cantidad prefijada de iteraciones. Palabras clave: potenciales evocados cerebrales, procesamiento de señales, filtros de Kalman, redes neuronales, neurociencia cognitiva.
In this paper we consider a strategy based on the values of the left one-sided maximal Hardy-Litt... more In this paper we consider a strategy based on the values of the left one-sided maximal Hardy-Littlewood operator to regulate the pulsating seeding of young fish in the case where two or more competitive species (eg perch and trout in lakes) interact; this strategy may occur as a natural from the point of view of those who propose seeding and also allows controlling the magnitudes resulting from competing species.
Fractals-complex Geometry Patterns and Scaling in Nature and Society, 2009
ABSTRACT The multifractal spectrum has been revealed recently as a very useful tool for the analy... more ABSTRACT The multifractal spectrum has been revealed recently as a very useful tool for the analysis of signals, especially in those coming from the measurement of physical variables in chaotic or critical systems with multifractal structure, and in which many phenomena interact in multiple scales. In addition, in this context, the presence of singularities of rapid oscillation, chirps, is frequently difficult to handle. In this work we propose a way for using &quot;wavelet leaders&quot;, avoiding the Legendre transform, for developing a new method capable of recognizing if a non-concave multifractal spectrum arises in a given signal, and is also capable of obtaining it in the case in which oscillating singularities appear, and so it succeeds where any other method fails.
In this work we analyze the correlation of the appearing T-wave alternans (TWA) with the shape (r... more In this work we analyze the correlation of the appearing T-wave alternans (TWA) with the shape (range) of the multifractal spectra of the ECG signals obtained with wavelet leaders based methods. A non-null correlation between the TWA occurring and lesser values for the Hölder exponent of maximum dimension has been observed, in agreement with the idea that the projection of TWA must have a non-despicable contribution in the higher scales of the multiresolution analysis of the signal. We are developing new algorithms capable to deal with non-concave multifractal spectra based in wavelet leaders projections, instead of existing methods that only gives concave spectra. These new algorithms will give a finer resolution of Hölder component of the signal and we hope that this richer information about the sharpness of the signal will allow better estimations of the magnitude of TWA and a closer relation between multifractal spectra and TWA occurring.
In this work we use α-bi-Lipschitz transformation of signals both from empirical and theoretical ... more In this work we use α-bi-Lipschitz transformation of signals both from empirical and theoretical sources to obtain new tests for the accomplishment of the multifractal formalisms associated with many methods (Wavelet Leaders, Wavelet Transform Modulus Maxima, Multifractal Detrended Fluctuation Analysis, Box Counting, and other) and we give improvements of the present algorithms that result numerically more trustworthy. Moreover the multifractal spectrum does not change in the theory, but as the numeric implementation of the computations may differ for discrete series so we can analyze its variation to study the stability of the proposed algorithms to compute it. In addition some single coefficients that have been proposed to quantify the whole irregularity of the signal are preserved by enough high α-bi-Lipschitz transformations. We exhibit the performance of the tests and the improvements of this methods not only in signals generated from deterministic (or sometimes random) numerical processes performed with the computer but also against series from empirical sources in which the multifractal spectrum and the irregularity coefficient were proven of utility both from the analysis and the segmentation of the signal in significant parts as series of Longwave outgoing radiation of tropical regions (and the consequent forecasting applications of precipitations) and certain series of EEG (from patients with crisis of brain absences for instance) and the ability to distinguish (and perhaps to predict) the beginning of the consecutive stages.
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Papers by Alvaro Corvalán