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arXiv · 2408.01060

Hilbert matrix operator acting between conformally invariant spaces

Carlo Bellavita·Georgios Stylogiannis
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Abstract

In this article we study the action of the the Hilbert matrix operator $\mathcal H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $\mathcal{H}$ from $H^\infty$ into $\text{BMOA}$ and we characterize the positive Borel measures $\mu$ such that $\mathcal H$ is bounded from $H^\infty$ into the conformally invariant Dirichlet space $M(\mathcal{D}_\mu )$. For particular measures $\mu$, we also provide the norm of $\mathcal{H}$ from $H^\infty$ into $M(\mathcal{D}_\mu )$.

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Carlo Bellavita, Georgios Stylogiannis. 2024-08-02. Hilbert matrix operator acting between conformally invariant spaces. https://doi.org/10.4153/s0008439524000948

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