## Annals of Functional Analysis

### A note on the essential norm of weighted composition operators on BMOA

#### Abstract

We give some new estimates for the essential norm of weighted composition operators on the space $\mathit{BMOA}$. As a corollary, we obtain a new characterization for the compactness of weighted composition operators on the space $\mathit{BMOA}$.

#### Article information

Source
Ann. Funct. Anal., Volume 7, Number 3 (2016), 521-528.

Dates
Accepted: 1 March 2016
First available in Project Euclid: 22 August 2016

https://projecteuclid.org/euclid.afa/1471876888

Digital Object Identifier
doi:10.1215/20088752-3625066

Mathematical Reviews number (MathSciNet)
MR3540449

Zentralblatt MATH identifier
1345.30080

Subjects
Primary: 30H35: BMO-spaces
Secondary: 47B33: Composition operators

#### Citation

Li, Songxiao; Liu, Xiaosong. A note on the essential norm of weighted composition operators on BMOA. Ann. Funct. Anal. 7 (2016), no. 3, 521--528. doi:10.1215/20088752-3625066. https://projecteuclid.org/euclid.afa/1471876888

#### References

• [1] P. Bourdon, J. Cima, and A. Matheson, Compact composition operators on BMOA, Trans. Amer. Math. Soc. 351 (1999), no. 6, 2183–2196.
• [2] F. Colonna, Weighted composition operators between $H^{\infty}$ and BMOA, Bull. Korean Math. Soc. 50 (2013), no. 1, 185–200.
• [3] C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Stud. Adv. Math., CRC Press, Boca Raton, Fla., 1995.
• [4] P. Galindo, J. Laitila, and M. Lindström, Essential norm estimates for composition operators on BMOA, J. Funct. Anal. 265 (2013), no. 4, 629–643.
• [5] J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
• [6] J. Laitila, Weighted composition operators on BMOA, Comput. Methods Funct. Theory 9 (2009), no. 1, 27–46.
• [7] J. Laitila and M. Lindström, The essential norm of a weighted composition operator on BMOA, Math Z. 279 (2015), no. 1–2, 423–434.
• [8] J. Laitila, P. Nieminen, E. Saksman, and H. Tylli, Compact and weakly compact composition operators on BMOA, Complex Anal. Oper. Theory 7 (2013), no. 1, 163–181.
• [9] W. Smith, Compactness of composition operators on BMOA, Proc. Amer. Math. Soc. 127 (1999), no. 9, 2715–2725.
• [10] H. Wulan, Compactness of composition operators on BMOA and VMOA, Sci. China Ser. A 50 (2007), no. 7, 997–1004.
• [11] H. Wulan, D. Zheng, and K. Zhu, Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc. 137 (2009), no. 11, 3861–3868.
• [12] K. Zhu, Operator Theory in Function Spaces, Math. Surveys Monogr. 138, Amer. Math. Soc., Providence, 2007.