Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of $\beta$-Ces\`aro operators on $\alpha$-Bloch space   For each $ \alpha > 0 $, the $\alpha$-Bloch space is consisting of all
analytic functions $f$ on the unit disk satisfying $ \sup_{|z|<1}
(1-|z|^2)^\alpha |f'(z)| < + \infty.$ In this paper, we consider the following
complex integral operator, namely the $\beta$-Ces\`{a}ro operator
\begin{equation}
  C_\beta(f)(z)=\int_{0}^{z}\frac{f(w)}{w(1-w)^{\beta}}dw \nonumber
\end{equation} and its generalization, acting from the $\alpha$-Bloch space to
itself, where $f(0)=0$ and $\beta\in\mathbb{R}$. We investigate the boundedness
and compactness of the $\beta$-Ces\`{a}ro operators and their generalization.
Also we calculate the essential norm and spectrum of these operators.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph