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arXiv · 1912.09377

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

Michel Alexis·Alexander Aptekarev·Sergey Denisov
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Abstract

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.

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Michel Alexis, Alexander Aptekarev, Sergey Denisov. 2019-12-19. Continuity of weighted operators, Muckenhoupt $A_p$ weights, and Steklov problem for orthogonal polynomials. https://arxiv.org/abs/1912.09377

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