Norm estimates relating polynomials and their derivatives

Rubinstein, Zalman

doi:10.1090/S0002-9939-1980-0574512-1

Norm estimates relating polynomials and their derivatives
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by Zalman Rubinstein

Proc. Amer. Math. Soc. 80 (1980), 78-82

DOI: https://doi.org/10.1090/S0002-9939-1980-0574512-1

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Abstract:

Inequalities bounding ${L_p}(p > 0)$ norms of a polynomial by suitable norms of the derivative of the polynomial and an auxiliary function are obtained for the classes of polynomials whose zeros lie on the unit circumference or in the interior or the exterior of the unit disk. All the inequalities are best possible and generalize several known estimates in particular cases.

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