Glasnik Matematicki, Vol. 32, No.2 (1997), 213-215.

AN L^p INEQUALITY FOR SELF-INVERSIVE POLYNOMIALS

N. K. Govil

Abstract.   Let denote the set of all polinomials p(z) of degree at most n. Here we show that if p and satisfies p(z) = zⁿp(1/z), then

n/2 ||p||_δ ||p'||_δ n C_δ^1/δ ||p||_δ,

where C_δ = (2^-δ π Γ(δ/2 + 1)) / (Γ(δ/2 + 1/2)). The inequality on the right hand side is best possible and the equality holds for polynomials p(z) = a + bzⁿ, |a| = |b|.

1991 Mathematics Subject Classification.   30A10, 30C10, 30E10.

Key words and phrases.   Inequalities in the complex domain, polynomials, approximation in the complex domain.