A Bernstein type \(L^p\) inequality for a certain class of polynomials (Q1269678)

Let \(\|\cdot\|_p\) be the \(L^p\)-norm on the unit circle. Let \(Q(z)= \sum_{k=m}^n a_kz^k\), and let \(Q(z)\neq 0\) on \(| z|< K\), \(K>1\). The authors give an upper estimate of \(\| Q'\|_p/\| Q\|_p\). They extend a result of \textit{M. A. Qazi} [Proc. Am. Math. Soc. 115, No. 2, 337-343 (1992; Zbl 0772.30006)], who proved the case \(p=\infty\).