Generalizations of Some Zygmund-type Integral Inequalities for Polar Derivatives of a Complex Polynomial

Abdullah Mir

We prove some results for algebraic polynomials in the complex plane that relate the $L^\gamma$-norm of the polar derivative of a complex polynomial and the polynomial under some conditions. The obtained results include several interesting generalizations of some Zygmund-type integral inequalities for polynomials and derive polar derivative analogues of some classical Bernstein-type inequalities for the sup-norms on the unit disk as well.