SOME NEW GENERALIZATIONS OF ZYGMUND-TYPE INEQUALITIES FOR POLYNOMIALS

摘要

In this paper, we consider a problem of investigating the dependence of on ||P(Rz)||αp(rz)+β{(R+1/r+1)~n-|α|}||_p on ||p(z)||_pfor arbitrary real or complex numbers a, ? with |a| = 1, |?|=l,R>r=l, p > 0 and present certain sharp compact generalizations of some well-known Zygmund-type inequalities for polynomials, from which a variety of interesting results follows as special cases.