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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Two-weight norm inequalities for Cesàro means of Laguerre expansions
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by Benjamin Muckenhoupt and David W. Webb PDF
Trans. Amer. Math. Soc. 353 (2001), 1119-1149 Request permission

Abstract:

Two-weight $L^{p}$ norm inequalities are proved for Cesàro means of Laguerre polynomial series and for the supremum of these means. These extend known norm inequalities, even in the single power weight and “unweighted” cases, by including all values of $p\geq 1$ for all positive orders of the Cesàro summation and all values of the Laguerre parameter $\alpha >-1$. Almost everywhere convergence results are obtained as a corollary. For the Cesàro means the hypothesized conditions are shown to be necessary for the norm inequalities. Necessity results are also obtained for the norm inequalities with the supremum of the Cesàro means; in particular, for the single power weight case the conditions are necessary and sufficient for summation of order greater than one sixth.
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Additional Information
  • Benjamin Muckenhoupt
  • Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019
  • Email: muckenho@math.rutgers.edu
  • David W. Webb
  • Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614-3504
  • Email: dwebb@condor.depaul.edu
  • Received by editor(s): May 28, 1999
  • Published electronically: November 14, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 1119-1149
  • MSC (1991): Primary 42C10
  • DOI: https://doi.org/10.1090/S0002-9947-00-02729-X
  • MathSciNet review: 1804415