Some Lp Inequalities Concerning the Polar Derivative of a Polynomial

摘要

For the class of lacunary polynomials , 1 ≤μ ≤ n, of degree n having all their zeros in |z| ≤ k where k ≤ 1, Rather and Mir [12] proved that for α ∈ C with |α| ≥ k~μ,where D_αP(z) = nP(z) + (α - z)P'(z) denote the polar derivative of the polynomial P(z) of degree n with respect to a point α ∈ C. In this paper, we obtain L_p mean extension of above inequality.