Jacobi transplantation revisited |
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| Authors: | Óscar Ciaurri Adam Nowak Krzysztof Stempak |
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| Institution: | 1. Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004, Logro?o, Spain
2. Instytut Matematyki i Informatyki, Politechnika Wroc?awska, Wyb. Wyspiańskiego 27, 50-370, Wroc?aw, Poland
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| Abstract: | A transplantation theorem for Jacobi series proved by Muckenhoupt is reinvestigated by means of a suitable variant of Calderón–Zygmund
operator theory. An essential novelty of our paper is weak type (1,1) estimate for the Jacobi transplantation operator, located
in a fairly general weighted setting. Moreover, L
p
estimates are proved for a class of weights that contains the class admitted in Muckenhoupt’s theorem.
Research of ó. Ciaurri and K. Stempak was supported by the grant MTM2006-13000-C03-03 of the DGI. Research of A. Nowak and
K. Stempak was supported by MNiSW Grant N201 054 3214285. |
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| Keywords: | Jacobi polynomials Transplantation Local Calderón– Zygmund operators Weighted norm inequalities Darboux type formula |
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