Back to Search
Start Over
Mean Lipschitz spaces and a generalized Hilbert operator
- Source :
- Collect. Math. (2019) 70 (1), 59-69
- Publication Year :
- 2017
-
Abstract
- If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu _{n, k})_{n,k\ge 0}$ with entries $\mu _{n, k}=\mu _{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes the moment of order $n$ of $\mu $. This matrix induces formally the operator $$\mathcal{H}_\mu (f)(z)= \sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} \mu_{n,k}{a_k}\right)z^n$$ on the space of all analytic functions $f(z)=\sum_{k=0}^\infty a_kz^k$, in the unit disc $\mathbb{D} $. This is a natural generalization of the classical Hilbert operator. In this paper we study the action of the operators $\mathcal H_\mu $ on mean Lipschitz spaces of analytic functions.<br />Comment: 11 pages, 0 figures
- Subjects :
- Mathematics - Complex Variables
30H10
Subjects
Details
- Database :
- arXiv
- Journal :
- Collect. Math. (2019) 70 (1), 59-69
- Publication Type :
- Report
- Accession number :
- edsarx.1707.08775
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s13348-018-0217-y