# Moscow Mathematical Journal

Volume 16, Issue 4, October–December 2016 pp. 641–649.

A New Formula for Berezin Transforms Attached to Generalized Bergman Spaces on the Unit Ball 𝔹^{n}

**Authors**:
Abdelhamid Boussejra (1) and Zouhaïr Mouayn (2)

**Author institution:**(1) Department of Mathematics, Faculty of Sciences,
Ibn Tofail University, PO Box. 133, Kénitra, Morocco.

(2) Department of Mathematics, Faculty of Sciences & Technics (M'Ghila), PO Box. 523, Béni Mellal, Morocco.

**Summary: **

To each generalized Bergman space on the unit ball a Berezin transform is attached. We add a new formula representing this transform as a function of the Laplace–Beltrami operator by using the Fourier–Helgason transform.

2010 Math. Subj. Class. 43A32, 47B35, 47G10, 81Q35.

**Keywords:**Generalized Bergman spaces, Berezin transforms, magnetic Schrödinger operator, Laplace–Beltrami operator, Fourier–Helgason transform.

Contents Full-Text PDF