Generalized Hilbert Operators Acting from Hardy Spaces to Weighted Bergman Spaces
Abstract
Let $\mu$ be a positive Borel measure on the interval [0,1). For $α$>0, define the generalized Hankel matrix $\mathcal{H}_{\mu,α}=(\mu_{n,k,α})_{n,k≥0}$ having entries $\mu_{n,k,α}= \int_{[0,1)}\frac{\Gamma(n+\alpha)}{n!\Gamma(\alpha)}t^{n+k}d\mu(t),$ which formally induces the operator $$\mathcal {H}_{\mu,α}(f)(z)=\sum\limits_{n=0}^∞ \big(\sum\limits_{k=0}^∞=\mu_{n,k,α}a_k\big)z^n$$ on the space for all analytic functions $f(z)=\sum_{k=0}^∞a_kz^k$ in the unit disk $\mathbb{D}.$ We characterize the measures $\mu$ such that $\mathcal {H}_{\mu,α}=\int_{[0,1)}f(t)/(1−tz)^α d\mu(t)$ for all $f$ in the Hardy spaces $H^p(0< p
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Topics in Algebra
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Journal of Mathematical Study
- Publisher
- Global Science Press
- Volume
- 59
- Issue
- 2
- Pages
- 218–231
- Publication date
- 9 July 2026
- Language
- EN