Stevi' c-Sharma ‎type ‎‎operator ‎from Besov space into Zygmund space

Document Type : Original Paper

Authors

1 Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran

2 Department of Mathematics, University of Isfahan, Isfahanو Iran.

Abstract

Let‎ $H(mathbb{D})‎$ ‎be ‎the ‎space ‎of ‎all ‎analytic ‎functions ‎on‎ ‎$mathbb{D}‎$. ‎For ‎‎$‎u,vin H(mathbb{D})‎$ ‎and ‎self-map ‎‎$‎psi‎(‎psi(mathbb{D}‎)subset ‎mathbb{‎D}‎‎)‎$‎‎‎ the‎ Stevi' c-Sharma ‎type ‎operator ‎is ‎defined ‎as ‎follows‎

‎begin{align*}‎

‎T_{u‎, ‎v‎, ‎psi}f(z) = u(z) f{(psi(z))}‎+ ‎v(z) f'(psi(z))‎ ,‎quad fin H(mathbb{D} )‎, ‎quad zin mathbb{D}‎.

‎end{align*‎}‎

‎In ‎this ‎paper, ‎we ‎study ‎boundedness ‎and ‎compactness ‎of‎ Stevi' c-Sharma ‎type ‎‎operator ‎from Besov space into Zygmund ‎space ‎and ‎we ‎obtain ‎some ‎equivalence ‎conditions ‎for‎ boundedness ‎and ‎compactness ‎of ‎such ‎operator.

Keywords

Main Subjects


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Volume 11, Issue 3
September 2021
Pages 573-584
  • Receive Date: 07 May 2021
  • Revise Date: 29 July 2021
  • Accept Date: 10 September 2021
  • First Publish Date: 18 September 2021