Schrödinger type singular integrals : weighted estimates for p = 1

• Autores: Bongioanni, Bruno; Cabral, Enrique Adrián; Harboure, Eleonor Ofelia
• Año de publicación: 2016
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Mathematische Nachrichten, 2016, vol. 289, no. 11-12, p. 1341-1369.
• Materia: Schrödinger operator; Hardy spaces; Weights
• Institución: Universidad Nacional del Nordeste

Fil: Bongioanni, Bruno. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina.
Fil: Bongioanni, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral; Argentina.
Fil: Cabral, Enrique Adrián. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.
Fil: Harboure, Eleonor Ofelia. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina.
Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral; Argentina.
A critical radius function ρ assigns to each x ∈ Rd a positive number in a way that its variation at different points is somehow controlled by a power of the distance between them. This kind of function appears naturally in the harmonic analysis related to a Schrodinger operator ̈ − + V with V a non-negative potential satisfying some specific reverse Holder condition. For a family of singular integrals associated with such critical radius ̈ function, we prove boundedness results in the extreme case p = 1. On one side we obtain weighted weak (1, 1) results for a class of weights larger than Muckenhoupt class A1. On the other side, for the same weights, we prove continuity from appropriate weighted Hardy spaces into weighted L1. To achieve the latter result we define weighted Hardy spaces by means of a ρ-localized maximal heat operator. We obtain a suitable atomic decomposition and a characterization via ρ-localized Riesz Transforms for these spaces. For the case of ρ derived from a Schrodinger operator, we obtain new estimates for many of the operators appearing in [27].