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 Bn be the open unit ball in Cn and Bn2=Bn×Bn. The symmetric lifting operator which lifts analytic functions from H(Bn) to H(Bn2) is defined as follow
L(f)(z,w)=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
2023
Pages 155-160

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