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arXiv · 1805.07804

Norm estimates of weighted composition operators pertaining to the Hilbert Matrix

Mikael Lindström·Santeri Miihkinen·Niklas Wikman
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Abstract

Very recently, Božin and Karapetrović solved a conjecture by proving that the norm of the Hilbert matrix operator $\mathcal{H}$ on the Bergman space $A^p$ is equal to $\fracπ{\sin(\frac{2π}{p})}$ for $2 < p < 4.$ In this article we present a partly new and simplified proof of this result. Moreover, we calculate the exact value of the norm of $\mathcal{H}$ defined on the Korenblum spaces $H^\infty_α$ for $0 < α\le 2/3$ and an upper bound for the norm on the scale $2/3 < α< 1$.

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Mikael Lindström, Santeri Miihkinen, Niklas Wikman. 2018-05-20. Norm estimates of weighted composition operators pertaining to the Hilbert Matrix. https://arxiv.org/abs/1805.07804

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