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

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 $w$ be...

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Veröffentlicht in:International mathematics research notices 2022-04, Vol.2022 (8), p.5935-5972
Hauptverfasser: Alexis, Michel, Aptekarev, Alexander, Denisov, Sergey
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnaa249