Majorization of polynomials on the plane

We prove that for every χ−1, 1] and every real algebraic polynomial f of degree n such that |f(t): 1 on −1, 1], the following inequality takes place on the complex plane |f(x+iy)||T_n(1+iy)|,−∞y∞ where T_n is the Tchebycheff polynomial. This implies easily Vladimir Markov inequality.