Bergman and Dirichlet spaces in the unit ball and symmetric lifting operator

Document Type : Original Article

Authors

1 Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran

2 Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran

Abstract

Let $\mathbb{B}_n$ be the open unit ball in $\mathbb{C}^n$ and $\mathbb{B}_n^2 = \mathbb{B}_n \times \mathbb{B}_n$. The symmetric lifting operator which lifts analytic functions from $H(\mathbb{B}_n)$ to $H(\mathbb{B}_n^2)$ is defined as follow
\[
L(f)(z,w) = \frac{f(z) - f(w)}{z-w}.
\]
In this paper we investigate the action of symmetric lifting operator on the Bergman space in the unit ball. Also, we state a characterization for Dirichlet space and consider symmetric lifting operator on the Dirichlet space in the unit ball.

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References

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AUT Journal of Mathematics and Computing
Volume 4, Issue 2
March 2023
Pages 155-160

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