Area operators on large Bergman spaces

Authors

  • Hicham Arroussi University of Helsinki, Department of Mathematics and Statistics, and University of Reading, Department of Mathematics and Statistics
  • Jari Taskinen University of Helsinki, Department of Mathematics and Statistics
  • Cezhong Tong Hebei University of Technology, Institute of Mathematics
  • Zixing Yuan Wuhan University, School of Mathematics and Statistics

Keywords:

Bergman space, tent space, area operator

Abstract

We completely characterize those positive Borel measures μ on the open unit disk D for which the area operator Aμ:AφpLq(T) is bounded. Here, the indices 0<p,q< are arbitrary and φ belongs to a certain class W0 of exponentially decreasing weights. Accordingly, the proofs require techniques adapted to such weights, like tent spaces, Carleson measures for Aφp-spaces, Kahane–Khintchine inequalities, and decompositions of the unit disc by (ρ,r)-lattices, which differ from the conventional decompositions into subsets with essentially constant hyperbolic radii.
Section
Articles

Published

2024-12-04

How to Cite

Arroussi, H., Taskinen, J., Tong, C., & Yuan, Z. (2024). Area operators on large Bergman spaces. Annales Fennici Mathematici, 49(2), 731–749. https://doi.org/10.54330/afm.153073