Geodesic
Hilbert matrix operator acting between conformally invariant spaces
Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 550-567

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In this article, we study the action of the the Hilbert matrix operator $H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $H$ from $H^\infty $ into $\text {BMOA}$ and we characterize the positive Borel measures $\mu $ such that $H$ is bounded from $H^\infty $ into the conformally invariant Dirichlet space $M(D_\mu )$. For particular measures $\mu $, we also provide the norm of $H$ from $H^\infty $ into $M(D_\mu )$.
DOI : 10.4153/S0008439524000948
Mots-clés : Hilbert matrix operator, conformally invariant Banach spaces, analytic bounded mean oscillations, conformally invariant Dirichlet spaces 
Bellavita, Carlo; Stylogiannis, Georgios. Hilbert matrix operator acting between conformally invariant spaces. Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 550-567. doi: 10.4153/S0008439524000948
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     title = {Hilbert matrix operator acting between conformally invariant spaces},
     journal = {Canadian mathematical bulletin},
     pages = {550--567},
     year = {2025},
     volume = {68},
     number = {2},
     doi = {10.4153/S0008439524000948},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000948/}
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