Artículo
Behaviour of Schrödinger Riesz transforms over smoothness spaces
Fecha de publicación:
01/2023
Editorial:
Academic Press Inc Elsevier Science
Revista:
Journal of Mathematical Analysis and Applications
ISSN:
0022-247X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
As it was shown by Shen, the Riesz transforms associated to the Schrödinger operator L = −Δ + V are not bounded on Lp(Rd)-spaces for all p, 1 < p < ∞, under the only assumption that the potential satisfies a reverse Hölder condition of order d/2, d ≥ 3. Furthermore, they are bounded only for p in some finite interval of the type (1, p0), so it can not be expected to preserve regularity spaces. In this work we search for some kind of minimal additional conditions on the potential in order to obtain boundedness on appropriate weighted BMO type regularity spaces for all first and second order Riesz transforms, namely for the operators ∇L−1/2, V 1/2L−1/2, ∇2L−1, V L−1 and V 1/2∇L−1. We also explore to what extent such extra conditions are also necessary.
Palabras clave:
REGULARITY SPACES
,
RIESZ TRANSFORMS
,
SCHRÖDINGER OPERATOR
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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; Behaviour of Schrödinger Riesz transforms over smoothness spaces; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 517; 2; 1-2023; 1-31
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