Bernstein-Type Integral Inequalities for a Certain Class of Polynomials-II

In this paper, we establish some new inequalities in the plane that are inspired by some classical Bernstein-type inequalities that relate the sup-norm of a polynomial to that of its derivative on the unit circle. The obtained results relate the Lγ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^\gamma $$\end{document}-norm of the polar derivative and the polynomial. Our results besides derive polar derivative analogues of some classical Bernstein-type inequalities also include several interesting generalizations and refinements of some integral-norm inequalities for polynomials, as well.