Jacobi Transplantations and Weyl Integrals

• Viktor Kolyada ^[1] ; Luz Roncal Gómez ^[2]
  1. [1] Karlstad University

     Karlstad University

     Suecia

     
  2. [2] Universidad de La Rioja

     Universidad de La Rioja

     Logroño, España

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 61, Fasc. 2, 2010, págs. 205-221
• Idioma: español
• DOI: 10.1007/BF03191242
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• Resumen

  • 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)).