Alexis, Michel; Aptekarev, Alexander; Denisov, Sergey Continuity of weighted operators, Muckenhoupt \(A_p\) weights, and Steklov problem for orthogonal polynomials. (English) Zbl 1487.42059 Int. Math. Res. Not. 2022, No. 8, 5935-5972 (2022). Summary: We consider weighted operators acting on \(L^p(\mathbb{R}^d)\) and show that they depend continuously on the weight \(w\in A_p(\mathbb{R}^d)\) in the operator topology. Then, we use this result to estimate \(L^p_w(\mathbb{T})\) norm of polynomials orthogonal on the unit circle when the weight \(w\) belongs to Muckenhoupt class \(A_2(\mathbb{T})\) and \(p>2\). The asymptotics of the polynomial entropy is obtained as an application. MSC: 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 42B30 \(H^p\)-spaces 47B38 Linear operators on function spaces (general) Keywords:Muckenhoupt class; Szegő function PDFBibTeX XMLCite \textit{M. Alexis} et al., Int. Math. Res. Not. 2022, No. 8, 5935--5972 (2022; Zbl 1487.42059) Full Text: DOI arXiv