Generalizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial

摘要

Some Zygmund-type integral inequalities for the polar derivatives of complex polynomials, inspired by the classical Bernstein-type inequalities that relate the uniform norms of polynomials and their derivatives on the unit circle, are investigated. The obtained results sharpen as well as generalize some already known $L^{delta }$-estimates between polynomials and their polar derivatives.