Average case weighted [formula omitted] Markov factors with doubling weights

Abstract

For weighted L2 spaces with doubling weights w on [−1,1] and norms ‖⋅‖2,w, the Markov factor on a polynomial P is defined by ‖P′‖2,w‖P‖2,w. We study this Markov factor on random polynomials with independent N(0,1) coefficients, and show that the upper bound of the average (expected) Markov factor is order degree to the 3∕2, as compared to the degree squared worst case upper bound.