We prove a few interesting inequalities for Lorentz polynomials including
Nikolskii-type inequalities. A highlight of the paper is a sharp Markov-type
inequality for polynomials of degree at most n with real coefficients and with
derivative not vanishing in the open unit disk. The result may be compared with
Erdos's classical Markov-type inequality (1940) for polynomials of degree at
most n having only real zeros outside the interval (-1,1)
