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Transactions of the American Mathematical Society

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Multiplier criteria of Marcinkiewicz type for Jacobi expansions


Authors: George Gasper and Walter Trebels
Journal: Trans. Amer. Math. Soc. 231 (1977), 117-132
MSC: Primary 42A18
DOI: https://doi.org/10.1090/S0002-9947-1977-0467139-8
MathSciNet review: 0467139
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Abstract: It is shown how an integral representation for the product of Jacobi polynomials can be used to derive a certain integral Lipschitz type condition for the Cesàro kernel for Jacobi expansions. This result is then used to give criteria of Marcinkiewicz type for a sequence to be multiplier of type (p, p), $ 1 < p < \infty $, for Jacobi expansions.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0467139-8
Keywords: Multipliers, Jacobi polynomials, ultraspherical polynomials, Cesàro kernel, Poisson kernel, fractional differences
Article copyright: © Copyright 1977 American Mathematical Society

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