Some remarks on Turán's inequality. II (Q1322311)

This is a sequel to a paper of the author [J. Approximation Theory 68, 45-48 (1992; Zbl 0752.41015)]. In this paper he examines how large the \(L^ p\) norm on \([-1,1]\) of the derivative of a real algebraic polynomial of degree at most \(n\) with zero only in \([-1,1]\) can be if the \(L^ q\) norm of the polynomial is 1, where \(0 < p \leq q \leq \infty\) and \(1 - {1 \over p} + {1 \over q} \geq 0\).