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A choice of Sobolev spaces associated with ultraspherical expansions
Betancor, J. J.
Fariña, J. C.
Rodríguez-Mesa, L.
Testoni, R.
Torrea, J. L.

Data: 2010
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 54 n. 1 (2010) p. 221-242, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_54110_13

22 p, 212.2 KB

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