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.
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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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Ciaurri, Ó., Nowak, A. & Stempak, K. Jacobi transplantation revisited. Math. Z. 257, 355–380 (2007). https://doi.org/10.1007/s00209-007-0128-1
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DOI: https://doi.org/10.1007/s00209-007-0128-1
Keywords
- Jacobi polynomials
- Transplantation
- Local Calderón–Zygmund operators
- Weighted norm inequalities
- Darboux type formula