# The Generalized Volterra Integral Operator and Toeplitz Operator on Weighted Bergman Spaces

@article{Du2021TheGV,
title={The Generalized Volterra Integral Operator and Toeplitz Operator on Weighted Bergman Spaces},
author={Juntao Du and Songxiao Li and Dan Qu},
journal={Mediterranean Journal of Mathematics},
year={2021},
volume={19}
}
• Published 2 September 2021
• Mathematics
• Mediterranean Journal of Mathematics
We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disc. A generalized Toeplitz operator is defined and the boundedness, compactness and Schatten class membership of this operator are investigated on the Hilbert weighted Bergman space. As an application, Schatten class membership of generalized Volterra integral operators are also characterized. Finally, we also get the characterizations of Schatten…

## References

SHOWING 1-10 OF 28 REFERENCES

• Mathematics
• 2018
Given a regular weight $$\omega$$ω and a positive Borel measure $$\mu$$μ on the unit disc $$\mathbb {D}$$D, the Toeplitz operator associated with $$\mu$$μ is \begin{aligned} {\mathcal {T}}_\mu • Mathematics The Journal of Geometric Analysis • 2018 Given some regular weight\omega $$ω on the unit disk$$\mathbb {D}$$D, let$$L^p_\omega $$Lωp be the space of all Lebesgue measurable functions on$$\mathbb {D}$$D for which$$\begin{aligned}
• Mathematics
• 1997
Let ${\bold D}$ denote the unit disk in the complex plane and let $m$ be the area Lebesgue measure on ${\bold D}$. Given a positive integrable function $w$ (a weight) on ${\bold D}$, let $L^p_{\rm • Mathematics • 2012 This monograph is devoted to the study of the weighted Bergman space$A^p_\om$of the unit disc$\D$that is induced by a radial continuous weight$\om$satisfying {equation}\label{absteq} • Mathematics Mathematische Zeitschrift • 2019 The zero sets of the Bergman space $$A^p_\omega$$Aωp induced by either a radial weight $$\omega$$ω admitting a certain doubling property or a non-radial Bekollé-Bonami type weight are characterized • Mathematics • 2014 Let $$A^p_\omega$$Aωp denote the Bergman space in the unit disc induced by a radial weight $$\omega$$ω with the doubling property$\$\int _{r}^1\omega (s)\,ds\le C\int _{\frac{1+r}{2}}^1\omega
This paper is based on the course \lq\lq Weighted Hardy-Bergman spaces\rq\rq\, I delivered in the Summer School \lq\lq Complex and Harmonic Analysis and Related Topics\rq\rq at the Mekrij\"arvi
Inspired by the study of generalized Cesaro operator T_g introduced by Aleman and Siskakis we study a variation of this operator,namely P(g,a) , depending on an analytic symbol g and an n - tuple of