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Teorema T1 a valores vectoriales con medidas no necesariamente doblantes: Aplicaciones

Pablo Sebastián Viola Beatriz Eleonora Viviani Carlos Alberto Cabrelli Tomás Fernando Godoy Felipe Joaquín Zó José Luis Torrea Hernández

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Resumen/Descripción – provisto por el repositorio digital
This Thesis includes the study of singular integral operators in the context of non-necessarily doubling measures and functions valued on a Hilbert space. In the first part of the Thesis a "T1 equals 0" type Theorem is proven, in the context of spaces of homogeneous type and for funcions valued on a Hilbert space. This result is applied to the square function operator associated to an identity aproximation on a space of homogeneous tuye. In the second part of the Thesis, singular integral operators associated to kernels satisfying size and smoothness integral conditions are studied, in the context of non-necessarily doubling measures in the n-dimensional euclidean space, for functions valued on a Hilbert space. Formulas and Lipschitz bounds are obtained for those operatores, generalizing the results obtained by Macías, Segovia y Torrea in the case of doubling measures. Also, under the "T1 equals 0" hypothesis, it is obtained that these operators have bounded extensions on spaces of square summable functions. Finally these results are applied to the study of oscillation operators associated to classical operators of the harmonic analysis.
Palabras clave – provistas por el repositorio digital

T1 theorem; Non-doubling measures; Vector valued; Singular integrals; Oscillation and variation operators; Teorema T1; Medidas no doblantes; Valores vectoriales; Integrales singulares; Operadores de oscilación y variación

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No requiere 2008 Biblioteca Virtual de la Universidad Nacional del Litoral (SNRD) acceso abierto

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tesis

Idiomas de la publicación

  • español castellano

País de edición

Argentina

Fecha de publicación