Jacobi Transplantations and Weyl Integrals
- Kolyada, Viktor 1
- Roncal Gómez, Luz 2
- 1 Department of Mathematics, Karlstad University, Universitetsgatan 1, 651 88 Karlstad, Sweden
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2
Universidad de La Rioja
info
ISSN: 0010-0757
Year of publication: 2010
Volume: 61
Fascicle: 2
Pages: 205-221
Type: Article
More publications in: Collectanea mathematica
Abstract
We prove that transplantations for Jacobi polynomials can bederived from representation of a special integral operator asfractional Weyl's integral. Furthermore, we show that, in a sense,Jacobi transplantation can be reduced to transplantations forultraspherical polynomials. As an application of these results, weobtain transplantation theorems for Jacobi polynomials in $\RealH^1$ and $\BMO.$ The paper gives an extension of the resultsobtained for ultraspherical polynomials by the first named author(MR2148530 (2006a:42045)).