7 research outputs found
Maximal operators associated with Generalized Hermite polynomials and function expansions
We study the weak and strong type boundedness of maximal heat?diffusion operators associated with the system of generalized Hermite polynomials and with two different systems of generalized Hermite functions. We also give a necessary background to define Sobolev spaces in this context.Fil: Forzani, Liliana Maria. Consejo Nacional de Invest.cientif.y Tecnicas. Centro Cientifico Tecnol - CONICET - Santa Fe. Instituto de Matematica Aplicada; Argentina; Universidad Nacional del Litoral. Facultad de Ingenieria Quimica;Fil: Sasso. Emanuela. Universita Di Genova; Italia;Fil: Scotto, Roberto AnÃbal. Consejo Nacional de Invest.cientif.y Tecnicas. Centro Cientifico Tecnol - CONICET - Santa Fe. Instituto de Matematica Aplicada; Argentina; Universidad Nacional del Litoral. Facultad de Ingenieria Quimica
Riesz transforms on variable Lebesgue spaces with Gaussian measure
We give sufficient conditions on variable exponent functions p : Rn → [1,∞) for which the higher-order Riesz transforms, associated with the Ornstein–Uhlenbeck semigroup, are bounded on Lp(·) (Rn, dγ ), where γ denotes the Gaussian measure.Fil: Dalmasso, EstefanÃa Dafne. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Scotto, Roberto AnÃbal. Universidad Nacional del Litoral. Facultad de IngenierÃa QuÃmica; Argentin
Dimension functions of Cantor sets
We estimate the packing measure of Cantor sets associated to nonincreasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets.Fil: Garcia, Ignacio Andres. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de IngenierÃa QuÃmica; ArgentinaFil: Molter, Ursula Maria. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Scotto, Roberto AnÃbal. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad Nacional del Litoral; Argentin
On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type independently of their orders.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Scotto, Roberto AnÃbal. Universidad Nacional del Litoral; Argentin
Weak type inequality for a family of singular integral operators related with the Gaussian measure
In this paper we study a family of singular integral operators that generalizes the higher order Gaussian Riesz Transforms and find the right weight w to make them continuous from L1(wdγ) into L1,∞(dγ), being dγ(x) = e-x2dx. Some boundedness properties of these operators had already been derived by Urbina (Ann Scuola Norm Sup Pisa Cl Sci 17(4):531-567, 1990) and Pérez (J Geom Anal 11(3):491-507, 2001).Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Scotto, Roberto AnÃbal. Universidad Nacional del Litoral; Argentin
Bellman functions and dimension free L p -estimates for the Riesz transforms in Bessel settings
In this article we prove dimension free ?boundedness of Riesz transforms associated with a Bessel differential operator. We obtain explicit estimates of the ?norms for the Bessel?Riesz transforms in terms of , establishing a linear behavior with respect to . We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator.Fil: Betancor, Jorge J.. Universidad de la Laguna. Departamento de Analisis Matematico; EspañaFil: Dalmasso, EstefanÃa Dafne. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Fariña, Juan C.. Universidad de la Laguna. Departamento de Analisis Matematico; EspañaFil: Scotto, Roberto AnÃbal. Universidad Nacional del Litoral. Facultad de IngenierÃa QuÃmica; Argentin