Abstract
In this paper, we characterize Carleson measure and
vanishing Carleson measure on Bergman spaces with
admissible weights in terms of t-Berezin transform
and averaging function as key tools. As an
application of the main results of this paper, we
characterize power bounded and power compact weighted
composition operators on Bergman spaces with admissible
weights.
Надано характеризацію міри Карлесона і
міри Карлесона, що прямує до нуля, на просторах Бергмана з
допустимими вагами в термінах $t$-перетворення
Березіна та функцією усереднення в якості
ключових інструментів. Як застосування основних
результатів цієї роботи надано характеризацію степенево
обмежених та степенево компактних зважених операторів
композиції на просторах Бергмана з допустимими вагами.
Key words: Weighted composition operator, Carleson measure,
power bounded, power compact and admissible weight.
Full Text
Article Information
| Title | Vanishing Carleson measures and power compact weighted
composition
operators |
| Source | Methods Funct. Anal. Topology, Vol. 28 (2022), no. 3, 259-273 |
| DOI | 10.31392/MFAT-npu26_3.2022.05 |
| MathSciNet |
MR4550662 |
| Milestones | Received 05/07/2022; Revised 16/10/2022 |
| Copyright | The Author(s) 2022 (CC BY-SA) |
Authors Information
Aakriti Sharma
Department of Mathematics, Central University of Jammu, Bagla, Rahya-Suchani, Samba 181143, India
Ajay K. Sharma
Department of Mathematics, Central University of Jammu, Bagla, Rahya-Suchani, Samba 181143, India
M. Mursaleen
Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Citation Example
Aakriti Sharma, Ajay K. Sharma, and M. Mursaleen, Vanishing Carleson measures and power compact weighted
composition
operators, Methods Funct. Anal. Topology 28
(2022), no. 3, 259-273.
BibTex
@article {MFAT1798,
AUTHOR = {Aakriti Sharma and Ajay K. Sharma and M. Mursaleen},
TITLE = {Vanishing Carleson measures and power compact weighted
composition
operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {28},
YEAR = {2022},
NUMBER = {3},
PAGES = {259-273},
ISSN = {1029-3531},
MRNUMBER = {MR4550662},
DOI = {10.31392/MFAT-npu26_3.2022.05},
URL = {http://mfat.imath.kiev.ua/article/?id=1798},
}
