Weighted Cesàro type operators on the weighted Bergman spaces in the unit ball
Abstract
In this paper, we study weighted Cesàro type operators 𝒞μ,βξ:Aαp(𝔹n) ⟶ Aαq(𝔹n) induced by measures on [0,1), and obtain boundedness characterizations throughout the range 0<p,q≤∞. We first extend the corresponding results on the unit disk to the unit ball in the range 1≤ p≤ q<∞. By means of atomic decomposition, we further treat the case 0<p<1 and p≤ q<∞, thereby obtaining a complete characterization for 0<p≤ q<∞. The latter result is new even in one dimension. For the range 0<q<p≤∞, we characterize the boundedness in terms of an integral condition involving the tail function of the inducing measure. This result is also new even on the unit disk. Finally, we characterize the boundedness of the corresponding operators when the target space is H∞(𝔹n).
Related
- Compact linear combination of composition operators on weighted Bergman-Orlicz spaces induced by doubling weights
- Quantum harmonic analysis and the Differential operators on weighted Bergman spaces of bounded symmetric domains
- Compact Toeplitz operators via the Berezin transform on radial weighted Bergman spaces
- Cesàro-type operators on average radial integrability spaces induced by doubling weights
- Bergman Kernels and Hankel Operators on Weighted Fock Spaces in Several Complex Variables
BibTeX
@misc{pan2026weighted,
title = {{Weighted Cesàro type operators on the weighted Bergman spaces in the unit ball}},
author = {Jiaxin Pan and Cezhong Tong and Zicong Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03243},
eprint = {2609.03243},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03243},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weighted Cesàro type operators on the weighted Bergman spaces in the unit ball
AU - Jiaxin Pan
AU - Cezhong Tong
AU - Zicong Yang
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03243
UR - https://arxiv.org/abs/2609.03243
AB - In this paper, we study weighted Cesàro type operators 𝒞_μ,β^ξ:A_α^p(𝔹_n) ⟶ A_α^q(𝔹_n) induced by measures on [0,1), and obtain boundedness characterizations throughout the range 0<p,q≤∞. We first extend the corresponding results on the unit disk to the unit ball in the range 1≤ p≤ q<∞. By means of atomic decomposition, we further treat the case 0<p<1 and p≤ q<∞, thereby obtaining a complete characterization for 0<p≤ q<∞. The latter result is new even in one dimension. For the range 0<q<p≤∞, we characterize the boundedness in terms of an integral condition involving the tail function of the inducing measure. This result is also new even on the unit disk. Finally, we characterize the boundedness of the corresponding operators when the target space is H^∞(𝔹_n).
ER -