H. Wulan

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math.CV2026

Hilbert matrix norms on weighted Bergman spaces: even exponents and a counterexample to the beta formula

Hasi Wulan, Mengmeng Zhou, Jian-Feng Zhu

Let $A_{I^} \pm^{p}$ be the weighted Bergman space on the unit disk, where $I^\pm > - 1$ . For $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{k} \in A_{I^} \pm^{p}$ , consider the Hilbert matrix operator $\mathcal{H}f(z)=\…

math.CV2026

The norm of the Hilbert matrix operator on Bergman spaces

Guanlong Bao, Liu Tian, Hasi Wulan

KarapetroviÄ conjectured that the norm of the Hilbert matrix operator on the Bergman space $A_{I^}^{p} \pm$ is equal to $I ¨ / sin ((2 + I^\pm) I ¨ / p)$ when $- 1 < I^\pm < p - 2$ . In this paper, we provide a…