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On some inequalities involving the zeros and weighted $L^p$ norms of polynomials


Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 130 (2002), 53-57
MSC (2000): Primary 30C10, 41A17
DOI: https://doi.org/10.1090/S0002-9939-01-06178-0
Published electronically: May 3, 2001
MathSciNet review: 1855619
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Abstract:

Using Parseval's identity and the Hardy-Littlewood-Pólya inequality on the maximal decreasing rearrangement, we establish some sharp inequalities involving the weighted $L^p$ norm and the zeros of polynomials.


References [Enhancements On Off] (What's this?)

  • 1. A.Kroo and I.Pritsker, A sharp version of Mahler's inequality for products of polynomials, Bull. London Math. Soc. 31(1999), 269-278. MR 99m:30008
  • 2. G.H.Hardy, J.E.Littlewood, and G.Pólya, Inequalities, Cambridge University Press, New York, 1934. 1952 edition MR 13:727e; 1988 edition MR 89d:26016

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Additional Information

Li-Chien Shen
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: shen@math.ufl.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06178-0
Received by editor(s): May 8, 2000
Published electronically: May 3, 2001
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society

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