Norm of difference of general polynomial weighted differentiation composition operators from Cauchy transform spaces into derivative Hardy spaces

Authors

  • Ebrahim Abbasi
  • Ajay K‎. ‎Sharma
  • Kamal ‎Khalilpour

DOI:

https://doi.org/10.30495/jme.v18i0.3074

Keywords:

B‎oundedness‎, ‎Cauchy transform space‎, ‎isometry‎, ‎norm‎

Abstract

‎In this paper‎, ‎we investigated boundedness of difference of general polynomial weighted differentiation composition operators from Cauchy transform spaces into function spaces $S=\{f:\ \ f'\in H^1\}$ and $S^2=\{f:\ \ f'\in H^2\}$ with derivative in Hardy spaces‎. ‎‎‎We also obtained an exact formula for the norm of this operator and prove that there is no composition isometry from the Cauchy transform spaces into $S$ and $S^2$ ‎spaces.‎

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Published

2025-02-05

Issue

Vol. 18

Section

Vol. 18, No. 10, (2024)

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