Two-weight norm inequalities for the Cesàro means of Hermite expansions
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- by Benjamin Muckenhoupt and David W. Webb PDF
- Trans. Amer. Math. Soc. 354 (2002), 4525-4537 Request permission
Abstract:
An accurate estimate is obtained of the Cesàro kernel for Hermite expansions. This is used to prove two-weight norm inequalities for Cesàro means of Hermite polynomial series and for the supremum of these means. These extend known norm inequalities, even in the single power weight and “unweighted” cases. An almost everywhere convergence result is obtained as a corollary. It is also shown that the conditions used to prove norm boundedness of the means and most of the conditions used to prove the boundedness of the Cesàro supremum of the means are necessary.References
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Additional Information
- Benjamin Muckenhoupt
- Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
- Email: muckenho@math.rutgers.edu
- David W. Webb
- Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614-7807
- Email: dwebb@condor.depaul.edu
- Received by editor(s): September 28, 2001
- Received by editor(s) in revised form: October 2, 2001
- Published electronically: July 2, 2002
- Additional Notes: The second author was supported by a URC grant at DePaul University.
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 4525-4537
- MSC (2000): Primary 42C10
- DOI: https://doi.org/10.1090/S0002-9947-02-03093-3
- MathSciNet review: 1926887