Open Access
2010 A Choice of Sobolev Spaces Associated with Ultraspherical Expansions
Jorge J. Betancor, Juan C. Fariña, Lourdes Rodríguez-Mesa, Ricardo Testoni, José L. Torrea
Publ. Mat. 54(1): 221-242 (2010).


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.


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Jorge J. Betancor. Juan C. Fariña. Lourdes Rodríguez-Mesa. Ricardo Testoni. José L. Torrea. "A Choice of Sobolev Spaces Associated with Ultraspherical Expansions." Publ. Mat. 54 (1) 221 - 242, 2010.


Published: 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1183.42026
MathSciNet: MR2603598

Primary: 42C05
Secondary: 42C15

Keywords: Sobolev Spaces , ultraspherical expansions

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.54 • No. 1 • 2010
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