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

References

[1] Abbasi E., A class of operator related weighted composition operators between Zygmund space, AUT J. Math. Com. 2(1) (2021) 17–25.
[2] Abbasi E. and Zhu X., Product-type operators from the Bloch space into Zygmund-type spaces, Bull. Iran. Math. Soc. (2021) doi 10.1007/s41980-020-00523-1.
[3] Colonna F. and Li S., Weighted composition operators from the Besov spaces to the Bloch spaces, Bull. Malays. Math. Sci. Soc. 36 (2013) 1027–1039.
[4] Colonna F. and Li S., Weighted composition operators from the Bloch space and the analytic Besov spaces into the Zygmund space, J. Operators, 2013 (2013), ID 154029-154038.
[5] Cowen C. C. and MacCluer B. D., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995.
[6] Liu Y. and Yu Y., On a Stević-Sharma operator from Hardy spaces to the logarithmic Bloch spaces, J. Inequal. Appl. 2015 2015:22, doi 10.1186/s13660-015-0547-1.
[7] Liu Y. and Yu Y., On Stević-Sharma type operators from the Besov spaces into the weighted-type space H1  , Math. Inequal. Appl. 22(3) (2019) 1037–1053.
[8] Stević S., Sharma A. and Bhat A., Essential norm of products of multiplications composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 218 (2011) 2386–2379.
[9] Stević S., Sharma A. and Bhat A., Products of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 217 (2011) 8115–8125.
[10] Wulan H., Zheng D. and Zhu K., Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc. 137 (2009) 3861–3868.
[11] Yu Y. and Liu Y., On Stević type operator fromH1 space to the logarithmic Bloch spaces, Complex Anal. Oper. Theory, 9(8) (2015) 1759–1780.
[12] Zhang F. and Liu Y., On the compactness of the Stević-Sharma operator on the logarithmic Bloch spaces, Math. Inequal. Appl. 19(2) (2016) 625–6426.
[13] Zhang F. and Liu Y., On a Stević-Sharma operator from Hardy spaces to Zygmund-type spaces on the unit disk, Complex Anal. Oper. Theory, 12(1) (2018) 81–100.
[14] Zhu K., Analytic Besov spaces, J. Math. Anal. Appl. 157(2) (1991) 318–336.
[15] Zhu K., Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23(3) (1993) 1143–1177.
[16] Zhu K., Operator Theory in Function Spaces, Amer. Math. Soc. second edition, 2007.
[17] Zhu X., Abbasi E. and Ebrahimi A., Product-type operators on the Zygmund space, Iran J. Sci. Technol. Trans. Sci. (2021) doi 10.1007/s40995-021-01138-9.
[18] Zhu X., Abbasi E. and Ebrahimi A., A class of operator-related composition operators from the Besov spaces into the Bloch space, Bull. Iran. Math. Soc. 47 (2021) 171–184.
Journal of Advanced Mathematical Modeling
Volume 11, Issue 3
September 2021
Pages 573-584

Files

History

  • Receive Date: 07 May 2021
  • Revise Date: 29 July 2021
  • Accept Date: 10 September 2021

Share

How to cite

Statistics