A choice of Sobolev spaces associated with ultraspherical expansions
Betancor, Jorge J. (Universidad de La Laguna. Departamento de Análisis Matemático)
Fariña, Juan C. (Universidad de La Laguna. Departamento de Análisis Matemático)
Rodríguez-Mesa, Lourdes (Universidad de La Laguna. Departamento de Análisis Matemático)
Testoni, Ricardo (Universidad Nacional del Sur (Argentina). Departamento de Matemática)
Torrea Hernández, J. L (Universidad Autónoma de Madrid. Departamento de Matemáticas)

Date:	2010
Abstract:	We discuss two possible definitions for Sobolev spaces associated with ultraspherical expansions. These definitions depend on the notion of higher order derivative. We show that in order to have an isomorphism between Sobolev and potential spaces, the higher order derivatives to be considered are not the iteration of the first order derivatives. Some discussions about higher order Riesz transforms are involved. Also we prove that the maximal operator for the Poisson integral in the ultraspherical setting is bounded on the Sobolev spaces.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Sobolev spaces ; Ultraspherical expansions
Published in:	Publicacions matemàtiques, V. 54 n. 1 (2010) p. 221-242, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/154826
DOI: 10.5565/PUBLMAT_54110_13

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