TY - JOUR
T1 - Sparse domination of weighted composition operators on weighted Bergman spaces
AU - Hu, Bingyang
AU - Li, Songxiao
AU - Shi, Yecheng
AU - Wick, Brett D.
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/3/15
Y1 - 2021/3/15
N2 - The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the A2 theorem for Calderón-Zygmund operators in harmonic analysis. Using this tool from harmonic analysis, some new characterizations are given for the boundedness and compactness of weighted composition operators acting between weighted Bergman spaces in the upper half plane. Moreover, we establish a new weighted type estimate for the holomorphic Bergman-class functions, for a new class of weights, which is adapted to Sawyer–testing conditions. We also extend our results to the unit ball B in Cn.
AB - The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the A2 theorem for Calderón-Zygmund operators in harmonic analysis. Using this tool from harmonic analysis, some new characterizations are given for the boundedness and compactness of weighted composition operators acting between weighted Bergman spaces in the upper half plane. Moreover, we establish a new weighted type estimate for the holomorphic Bergman-class functions, for a new class of weights, which is adapted to Sawyer–testing conditions. We also extend our results to the unit ball B in Cn.
KW - Sparse domination
KW - Weighted Bergman spaces
KW - Weighted composition operators
KW - Weighted estimates
UR - http://www.scopus.com/inward/record.url?scp=85097658535&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2020.108897
DO - 10.1016/j.jfa.2020.108897
M3 - Article
AN - SCOPUS:85097658535
SN - 0022-1236
VL - 280
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 6
M1 - 108897
ER -