Schrödinger type singular integrals : weighted estimates for p = 1

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...

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Autores principales: Bongioanni, Bruno, Cabral, Enrique Adrián, Harboure, Eleonor Ofelia
Formato: Artículo
Lenguaje:Inglés
Publicado: Wiley 2026
Materias:
Schrödinger operator
Hardy spaces
Weights
Acceso en línea:http://repositorio.unne.edu.ar/handle/123456789/60084
Aporte de:
RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) de Universidad Nacional del Nordeste
id I48-R184-123456789-60084
record_format dspace
spelling I48-R184-123456789-600842026-02-23T10:09:05Z Schrödinger type singular integrals : weighted estimates for p = 1 Bongioanni, Bruno Cabral, Enrique Adrián Harboure, Eleonor Ofelia Schrödinger operator Hardy spaces Weights 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]. 2026-02-20T11:41:09Z 2026-02-20T11:41:09Z 2016 Artículo Bongioanni, Bruno, Cabral, Enrique Adrián y Harboure, Eleonor Ofelia, 2016. Schrödinger type singular integrals : weighted estimates for p = 1. Mathematische Nachrichten. Weinheim: Wiley, vol. 289, no. 11-12, p. 1341-1369. E-ISSN 1522-2616. DOI ttps://doi.org/10.1002/mana.201400257 0025-584X http://repositorio.unne.edu.ar/handle/123456789/60084 eng ttps://doi.org/10.1002/mana.201400257 openAccess http://creativecommons.org/licenses/by-nc-nd/2.5/ar/ application/pdf p. 1341-1369 application/pdf Wiley Mathematische Nachrichten, 2016, vol. 289, no. 11-12, p. 1341-1369.
institution Universidad Nacional del Nordeste
institution_str I-48
repository_str R-184
collection RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
language Inglés
topic Schrödinger operator
Hardy spaces
Weights
spellingShingle Schrödinger operator
Hardy spaces
Weights
Bongioanni, Bruno
Cabral, Enrique Adrián
Harboure, Eleonor Ofelia
Schrödinger type singular integrals : weighted estimates for p = 1
topic_facet Schrödinger operator
Hardy spaces
Weights
description 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].
format Artículo
author Bongioanni, Bruno
Cabral, Enrique Adrián
Harboure, Eleonor Ofelia
author_facet Bongioanni, Bruno
Cabral, Enrique Adrián
Harboure, Eleonor Ofelia
author_sort Bongioanni, Bruno
title Schrödinger type singular integrals : weighted estimates for p = 1
title_short Schrödinger type singular integrals : weighted estimates for p = 1
title_full Schrödinger type singular integrals : weighted estimates for p = 1
title_fullStr Schrödinger type singular integrals : weighted estimates for p = 1
title_full_unstemmed Schrödinger type singular integrals : weighted estimates for p = 1
title_sort schrödinger type singular integrals : weighted estimates for p = 1
publisher Wiley
publishDate 2026
url http://repositorio.unne.edu.ar/handle/123456789/60084
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AT cabralenriqueadrian schrodingertypesingularintegralsweightedestimatesforp1
AT harboureeleonorofelia schrodingertypesingularintegralsweightedestimatesforp1
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