Small values of polynomials

and potentials with normalization

Author:
D. S. Lubinsky

Journal:
Proc. Amer. Math. Soc. **127** (1999), 529-536

MSC (1991):
Primary 30C10, 31A15; Secondary 41A17, 41A44, 30C85

DOI:
https://doi.org/10.1090/S0002-9939-99-04549-9

MathSciNet review:
1468199

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Abstract | References | Similar Articles | Additional Information

Abstract: For a polynomial of degree , normalized by the condition

we show that has at most , where is explicitly given and sharp for each . Similar estimates are given for other normalizations, such as , and for planar measure, and for generalized polynomials and potentials, thereby extending work of Cuyt, Driver and the author for . The relation to Remez inequalities is briefly discussed.

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Additional Information

**D. S. Lubinsky**

Affiliation:
Department of Mathematics, Witwatersrand University, Wits 2050, South Africa

Email:
036dsl@cosmos.wits.ac.za

DOI:
https://doi.org/10.1090/S0002-9939-99-04549-9

Keywords:
Cartan's lemma, capacity, polynomials, $L_p$ norm

Received by editor(s):
July 17, 1996

Received by editor(s) in revised form:
June 2, 1997

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1999
American Mathematical Society