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Vanishing Carleson measures and power compact weighted composition operators


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.


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Article Information

TitleVanishing Carleson measures and power compact weighted composition operators
SourceMethods Funct. Anal. Topology, Vol. 28 (2022), no. 3, 259-273
DOI10.31392/MFAT-npu26_3.2022.05
MathSciNet   MR4550662
Milestones  Received 05/07/2022; Revised 16/10/2022
CopyrightThe 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


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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},
}


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