Artículo
Boundedness and compactness for commutators of singular integrals related to a critical radius function
Fecha de publicación:
03/2021
Editorial:
Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral
Revista:
IMAL Preprints
e-ISSN:
2451-7100
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We work in the general framework of a family of singular integrals with kernels controlled in terms of a critical radius function ρ. This family models the harmonic analysis derived from the Schr¨odinger operator L = −∆ + V , where the non-negative potential V satisfies an appropriate reverse H¨older condition. For their commutators, we find sufficient conditions on the symbols for boundedness and/or compactness when acting on weighted Lp spaces. In all cases, the classes of symbols and weights are larger than their classical counterparts, BMO, CMO and Ap. When these general results are applied to the Schr¨odinger context, we obtain boundedness and compactness for commutators of operators like ∇L−1/2 , ∇2L−1 , V 1/2L−1/2 , V 1/2∇L−1 , V L−1 and Liα. As in Uchiyama’s classical paper, we give a full description of the class for compactness, CMO∞ρ , assuming ρ to be bounded. Finally, we provide examples showing that CMO is strictly contained in CMO∞ρ for any ρ, bounded or not.
Palabras clave:
Boundedness
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Articulos(IMAL)
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Citación
Bongioanni, Bruno; Harboure, Eleonor Ofelia; Quijano, Pablo; Boundedness and compactness for commutators of singular integrals related to a critical radius function; Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral; IMAL Preprints; 52; 3-2021; 1-28
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