Revista Matemática Iberoamericana


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Volume 34, Issue 4, 2018, pp. 1427–1441
DOI: 10.4171/RMI/1031

Published online: 2018-10-18

Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

Congwen Liu[1], Antti Perälä[2] and Lifang Zhou[3]

(1) University of Science and Technology of China, Hefei, Anhui, China
(2) Universitat de Barcelona, Spain
(3) Huzhou University, Huzhou, Zhejiang, China

We obtain new two-sided norm estimates for the family of Bergman-type projections arising from the standard weights $(1 − |z|^2)^{\alpha}$ where $\alpha > −1$. As $\alpha \to −1$, the lower bound is sharp in the sense that it asymptotically agrees with the norm of the Riesz projection. The upper bound is estimated in terms of the maximal Bergman projection, whose exact operator norm we calculate. The results provide evidence towards a conjecture that was posed very recently by the first author.

Keywords: Bergman projection, weighted Bergman space, operator norm

Liu Congwen, Perälä Antti, Zhou Lifang: Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound. Rev. Mat. Iberoam. 34 (2018), 1427-1441. doi: 10.4171/RMI/1031