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arXiv · 2410.16598

Norm of the Hilbert matrix operator between some spaces of analytic functions

Hao Hu·Shanli Ye
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Abstract

In this paper, we calculate the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ from the logarithmically weighted Korenblum space $H^\infty_{\alpha,\log}$ into Korenblum space $H^\infty_\alpha$, and from the Hardy space $H^\infty$ to the classical Bloch space $\mathcal{B}$. Furthermore, we compute the precise value of the norm on the logarithmically weighted Korenblum space $H^\infty_{\alpha,\log}$, and obtain both the lower and upper bounds of the norm on $\alpha$-Bloch space $\mathcal{B}^{\alpha}$. Finally, in the context of mapping from the Korenblum space $H^\infty_\alpha$ to the $(\alpha+1)$-Bloch space $\mathcal{B}^{\alpha+1}$, we establish the norm of $\mathcal{H}$.

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Hao Hu, Shanli Ye. 2024-10-22. Norm of the Hilbert matrix operator between some spaces of analytic functions. https://arxiv.org/abs/2410.16598

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