Resumen de Jacobi Transplantations and Weyl Integrals

Viktor Kolyada , Luz Roncal Gómez

• 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)).