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arXiv · 2410.18682

Hilbert matrix operator on bound analytic functions

Yuting Guo·Pengcheng Tang
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Abstract

It is well known that the Hilbert matrix operator $\mathcal {H}$ is bounded from $H^{\infty}$ to the mean Lipschitz spaces $\Lambda^{p}_{\frac{1}{p}}$ for all $1 1}\Lambda^{p}_{\frac{1}{p}}$. We also provide explicit upper and lower bounds for the norm of the Hilbert matrix $\mathcal {H}$ acting from $H^{\infty}$ to $\Lambda^{1.*}_{1}$. Additionally, we also characterize the positive Borel measures $\mu$ such that the generalized Hilbert matrix operator $\mathcal {H}_{\mu}$ is bounded from $H^{\infty}$ to the Hardy space $H^{q}$. This part is a continuation of the work of Chatzifountas, Girela and Pel\'{a}ez [J. Math. Anal. Appl. 413 (2014) 154--168] regarding $\mathcal {H}_{\mu}$ on Hardy spaces.

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Yuting Guo, Pengcheng Tang. 2024-10-24. Hilbert matrix operator on bound analytic functions. https://arxiv.org/abs/2410.18682

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