Artículo
Bessel Potentials in Ahlfors Regular Metric Spaces
Fecha de publicación:
08/2016
Editorial:
Springer
Revista:
Potential Analysis
ISSN:
0926-2601
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this paper we introduce Bessel potentials and the Sobolev potential spaces resulting from them in the context of Ahlfors regular metric spaces. The Bessel kernel is defined using a Coifman type approximation of the identity, and we show integration against it improves the regularity of Lipschitz, Besov and Sobolev-type functions. For potential spaces, we prove density of Lipschitz functions, and several embedding results, including Sobolev-type embedding theorems. Finally, using singular integrals techniques such as the T1 theorem, we find that for small orders of regularity Bessel potentials are inversible, its inverse in terms of the fractional derivative, and show a way to characterize potential spaces, concluding that a function belongs to the Sobolev potential space if and only if itself and its fractional derivative are in Lp . Moreover, this characterization allows us to prove these spaces in fact coincide with the classical potential Sobolev spaces in the Euclidean case.
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Articulos(IMAL)
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Citación
Marcos, Miguel; Bessel Potentials in Ahlfors Regular Metric Spaces; Springer; Potential Analysis; 45; 2; 8-2016; 201-227
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