Complex equilibrium measure and Bernstein type theorems for compact sets in 𝑅ⁿ

Baran, Mirosław

doi:10.1090/S0002-9939-1995-1219719-6

Complex equilibrium measure and Bernstein type theorems for compact sets in $\textbf {R}^ n$
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Proc. Amer. Math. Soc. 123 (1995), 485-494 Request permission

Abstract:

The aim of this paper is to refine and develop further some results from a paper of Bedford and Taylor [Trans. Amer. Math. Soc. 294 (1986), 705-717]. The main result, a Bernstein type theorem, is an improvement of the classical Bernstein inequality \[ |p’(x)| \leq (\deg p){(1 - {x^2})^{ - 1/2}}{(\left \| p \right \|_{[ - 1,1]}^2 - {p^2}(x))^{1/2}},\] from the interval $[ - 1,1]$ to the multivariate case.

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