Continuity of weighted operators, Muckenhoupt A_p weights, and Steklov problem for orthogonal polynomials

2019/12/19 by Alexis, Michel, Aptekarev, Alexander, Denisov, Sergey
#33C45 (Primary) #42C05 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.09377

Abstract

We consider weighted operators acting on L^p(ℝ^d) and show that they depend continuously on the weight w∈ A_p(ℝ^d) in the operator topology. Then, we use this result to estimate L^p_w(\mathbbT) norm of polynomials orthogonal on the unit circle when the weight w belongs to Muckenhoupt class A₂(\mathbbT) and p>2. The asymptotics of the polynomial entropy is obtained as an application.

Related

• The sharp estimates on the orthogonal polynomials from the Steklov class
• On a problem by Steklov
• The Steklov problem and Remainder Estimates for Krein Systems generated by a Muckenhoupt weight
• On the norms and roots of orthogonal polynomials in the plane and L^p-optimal polynomials with respect to varying weights
• Asymptotics of the orthogonal polynomials for the Szego class with a polynomial weight