Continuity of Weighted Operators, Muckenhoupt Ap Weights, and Steklov Problem for Orthogonal Polynomials

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

Automated summary

This article considers the continuous dependence of weighted operators on L-p(R-d) space, and uses this result to estimate the norm of orthogonal polynomials on the unit circle. Additionally, the asymptotics of polynomial entropy is obtained as an application.