Wilfredo O. Urbina
Roosevelt University
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Featured researches published by Wilfredo O. Urbina.
arXiv: Classical Analysis and ODEs | 2012
A. Eduardo Gatto; Ebner Pineda; Wilfredo O. Urbina
Gaussian Lipschitz spaces Lip α(γ d ) and the boundedness properties of Riesz potentials, Bessel potentials and fractional derivatives there were studied in detail in Gatto and Urbina (On Gaussian Lipschitz Spaces and the Boundedness of Fractional Integrals and Fractional Derivatives on them, 2009. Preprint. arXiv:0911.3962v2). In this chapter we will study the boundedness of those operators on Gaussian Besov-Lipschitz spaces B p, q α(γ d ). Also, these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.
Archive | 2016
María Cristina Pereyra; Stefania Marcantognini; Alexander M. Stokolos; Wilfredo O. Urbina
Cora Sadosky fought many battles and in many fronts. She had tremendous convictions against many injustices, gender inequality, and discrimination in our society. She often took the flag of the underrepresented, underserved, and underestimated. She chose to fight many of her battles from within the mathematical community, sometimes even risking her own mathematical career. She showed a lot of courage in this sense and never worried about the consequences for her. She was never afraid to express her views. We are deeply saddened for her passing but through her teachings we celebrate her life. To remember her we choose to focus on personal experiences that are not so wellknown, particularly about her mentorship role and her unselfish devotion to help young mathematicians. Cora always wanted to help students who were interested in following a research career in mathematics. In particular she interacted with many students in Venezuela and in Argentina. In her years in Caracas, Cora was very influential on a group of Venezuelan mathematicians, Maŕıa Dolores Morán, Ramón Bruzual, Marisela Domı́nguez and Stefania Marcantognini, among others, and a Uruguayan mathematician, Rodrigo Arocena, that got their PhD degrees at the Universidad Central de Venezuela (UCV). She also aided others pursue their doctorates in the US, including Gustavo Ponce who went to Courant Institute in 1978 and later Cristina Pereyra who went to Yale University in 1987. Likewise, during her sabbatical year in Buenos Aires in 1984-1985 she helped many Argentinian mathematicians come to the US for their doctoral degrees; among them, José Zero who went to University of Pennsylvania, Estela Gavosto and Rodolfo Torres who went to Washington University, and Andrea Nahmod and Lucas Monzón who went to Yale University. Over the last thirty years Cora conducted her professional life in the US but she continued to be interested in mathematics in Argentina and Venezuela where she often visited Mischa Cotlar. She was always trying to help colleagues and students in those countries in any way she could. Three years ago Cora retired from Howard University where she had been a professor since 1980. With her husband, Daniel Goldstein, they moved to California to be closer to their daughter Cora Sol, son in law Tom, and beloved granddaughter Sasha. We remember here particular moments and aspects of her mentorship.
Quaestiones Mathematicae | 2018
Calixto P. Calderón; A. Susana Coré; Wilfredo O. Urbina
Abstract In this paper we shall be concerned with Hα summability, for 0 < α ≤ 2 of the Fourier series of arbitrary L1([−π, π]) functions. The methods employed here are a modification of the real variable ones introduced by J. Marcinkiewicz. The needed modifications give direct proofs of maximal theorems with respect to A1 weights. We also give a counter-example of a measure such that there is no convergence a.e. to the density of the measure. Finally, we present a Kakutani type of theorem, proving the ω*-density, in the space of of probability measures defined on [−π, π] of Borel measures for which there is no H2 summability a.e.
Journal of Function Spaces and Applications | 2018
Eduard Navas; Wilfredo O. Urbina
We develop a transference method to obtain the -continuity of the Gaussian-Littlewood-Paley -function and the -continuity of the Laguerre-Littlewood-Paley -function from the -continuity of the Jacobi-Littlewood-Paley -function, in dimension one, using the well-known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials.
Archive | 2017
Calixto P. Calderón; Wilfredo O. Urbina
In 1966 Cora Sadosky introduced a number of results in a remarkable paper “A note on Parabolic Fractional and Singular Integrals”, see Sadosky (Studia Math 26:295–302, 1966), in particular, a quasi homogeneous version of Sobolev’s immersion theorem was discussed in the paper. Later, C. P. Calderon and T. Kwembe, following those ideas and incorporating the context of Fabes-Riviere homogeneity (Fabes and Riviere, Studia Math 27:19–38, 1966), proved a similar results for potential operators with kernels having mixed homogeneity. Calderon-Kwembe’s (Dispersal models. X Latin American School of Mathematics (Tanti, 1991). Rev Un Mat Argent 37(3–4):212–229, 1991/1992) basic theorem was very much in the spirit of Sadosky’s result. The natural extension of Sadosky’s paper is nevertheless the joint paper by C. Sadosky and M. Cotlar (On quasi-homogeneous Bessel potential operators. In: Singular integrals. Proceedings of symposia in pure mathematics, Chicago, 1966. American Mathematical Society, Providence, 1967, pp 275–287) which constitutes a true tour de force through, what is now considered, local properties of solutions of parabolic partial differential equations. The tools are the introduction of “Parabolic Bessel Potentials” combined with mixed homogeneity local smoothness estimates.
Archive | 2016
María Cristina Pereyra; Stefania Marcantognini; Alexander M. Stokolos; Wilfredo O. Urbina
Preface -- Part I: Cora -- Cora Sadosky: her mathematics, mentorship, and professional contributions (Rodolfo Torres) -- Coras scholarly work: publications according to MathSciNet -- Remembrances and Photos (Steven Krantz, Maria Dolores (Lolo) Moran, Guido Weiss, Mike Wilson, Georgia Benkhart, Judy Green, Richard Bourgin, Daniel Szyld, Estela Gavosto, Andrea Nahmod, Maria Cristina Pereyra, Gustavo Ponce, Rodolfo Torres & Wilfredo Urbina) -- Part II: Harmonic and Complex Analysis, Banach and Metric Spaces, and Partial Differential Equations -- Higher-order elliptic equations in non-smooth domains: history and recent results (Svitlana Mayboroda) -- Victor Shapiro and the theory of uniqueness for multiple trigonometric series (Marshall Ash) -- A last conversation with Cora (Aline Bonami) -- Fourier multipliers of the homogeneous Sobolev space W1,1 (Aline Bonami) -- A Note on nonhomogeneous weighted div-curl lemmas (Der-Chen Chang, Galia Dafni & Hong Yue) -- A remark on bilinear square functions (Lukas Grafakos) -- Unique continuous for the elasticity system and a counterexample for second order elliptic systems (Carlos Kenig & Jenn-Nan Wang) -- Hardy spaces of holomorphic functions for domains in Cn with minimal smoothness (Loredana Lanzani & Eli Stein) -- On the preservation of eccentricities of Monge-Ampere sections (Diego Maldonado) -- BMO: oscillations, self-improvement, Gagliardo coordinate spaces and reverse Hardy inequalities (Mario Milman) -- Besov spaces, symbolic calculus and boundedness of bilinear pseudodifferential operators (Virginia Naibo & Jodi Herbert) -- Metric characterization of some classes of Banach spaces (Mikhail Ostrowski) -- On the IVP for the k-generalized Benjamin-Ono equation (Gustavo Ponce).
Archive | 2014
Constantine Georgakis; Alexander M. Stokolos; Wilfredo O. Urbina
Preface (Constantine Georgakis).- Remembrances and Silhouettes.- The Calderon brothers, a happy mathematical relation.- Calixto Calderon as I knew him.- An Appraisal of Calixto Calderons Work in Mathematical Biology.- Remarks on various generalized derivatives.- Some non standard applications of the Laplace method.- Fejer Polynomials and Chaos.- A note on Widders Inequality.- Solyanik Estimates in Harmonic Analysis.- Some open problems related with generalized Fourier series.- Modeling the Mechanics of Aneurysm Development and Rupture Computational Simulation of Aneurysm Evolution, Growth and Rupture.- Singular Integral Operators on C1 Manifolds and C1 Curvilinear Polygons.- Towards a unified theory of Sobolev inequalities.- Transference of fractional Laplacian regularity.- Local sharp maximal functions.- Weighted norm estimates for singular integrals with L log L kernels Regularity of weak solutions of some degenerate quasilinear equations.
Archive | 2014
Calixto P. Calderón; Wilfredo O. Urbina
In this paper we consider two nonstandard applications of the Laplace method. The first one is referred to the Inversion Formula of D.V. Widder and E.L. Post, from which a maximal theorem is proved. The second one is a special Calderon–Zygmund partition that gives us a genuine generalization of Natanson’s lemma in this context.
arXiv: Classical Analysis and ODEs | 2014
Robert DiMartino; Wilfredo O. Urbina
Archive | 2017
María Cristina Pereyra; Stefania Marcantognini; Alexander M. Stokolos; Wilfredo O. Urbina