Orthogonal polynomials on the circle for the weight w satisfying conditions: w,1/w in BMO(T)

TL;DR

This paper investigates the asymptotic behavior of monic orthogonal polynomials on the circle for weights with both the weight and its inverse in BMO, providing new insights into their properties and related entropy estimates.

Contribution

It establishes asymptotics of orthogonal polynomials for weights with both the weight and its inverse in BMO, a novel result in this context.

Findings

Asymptotics of monic orthogonal polynomials in L^p for 2<p<p_0

Estimates on uniform norm of the polynomials

Asymptotics for polynomial entropy

Abstract

In the case when the weight and its inverse belong to BMO(T), we prove the asymptotics of the monic orthogonal polynomials in L^p, 2<p<p_0. Immediate applications include the estimates on the uniform norm and asymptotics for the polynomial entropy.