## Abstract and Applied Analysis

### Products of Composition and Differentiation Operators from ${\mathcal{Q}}_{K}(p,q)$ Spaces to Bloch-Type Spaces

#### Abstract

We study the boundedness and compactness of the products of composition and differentiation operators from ${\mathcal{Q}}_{K}(p,q)$ spaces to Bloch-type spaces and little Bloch-type spaces.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 741920, 14 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745575

Digital Object Identifier
doi:10.1155/2009/741920

Mathematical Reviews number (MathSciNet)
MR2516017

#### Citation

Yang, Weifeng; Stevic, Stevo. Products of Composition and Differentiation Operators from ${\mathcal{Q}}_{K}(p,q)$ Spaces to Bloch-Type Spaces. Abstr. Appl. Anal. 2009 (2009), Article ID 741920, 14 pages. doi:10.1155/2009/741920. https://projecteuclid.org/euclid.aaa/1268745575

#### References

• A. L. Shields and D. L. Williams, Bonded projections, duality, and multipliers in spaces of analytic functions,'' Transactions of the American Mathematical Society, vol. 162, pp. 287--302, 1971. \setlengthemsep2pt
• X. Fu and X. Zhu, Weighted composition operators on some weighted spaces in the unit ball,'' Abstract and Applied Analysis, vol. 2008, Article ID 605807, 8 pages, 2008.
• Z. Hu and S. Wang, Composition operators on Bloch-type spaces,'' Proceedings of the Royal Society of Edinburgh A, vol. 135, no. 6, pp. 1229--1239, 2005.
• S. Stević, Norm of weighted composition operators from Bloch space to $H_\mu ^\infty$ on the unit ball,'' Ars Combinatoria, vol. 88, pp. 125--127, 2008.
• S. Stević, On a new operator from $H^\infty$ to the Bloch-type space on the unit ball,'' Utilitas Mathematica, vol. 77, pp. 257--263, 2008.
• H. Wulan and J. Zhou, $\mathcalQ_K$ type spaces of analytic functions,'' Journal of Function Spaces and Applications, vol. 4, no. 1, pp. 73--84, 2006.
• R. Zhao, On a general family of function spaces,'' Annales Academi$\ae$ Scientiarum Fennic$\ae$. Mathematica Dissertationes, no. 105, pp. 1--56, 1996.
• M. Kotilainen, On composition operators in $\mathcalQ_K$ type spaces,'' Journal of Function Spaces and Applications, vol. 5, no. 2, pp. 103--122, 2007.
• C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995.
• S. Stević, Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball,'' Applied Mathematics and Computation, vol. 212, no. 2, pp. 499--504, 2009.
• R. A. Hibschweiler and N. Portnoy, Composition followed by differentiation between Bergman and Hardy spaces,'' The Rocky Mountain Journal of Mathematics, vol. 35, no. 3, pp. 843--855, 2005.
• S. Ohno, Products of composition and differentiation between Hardy spaces,'' Bulletin of the Australian Mathematical Society, vol. 73, no. 2, pp. 235--243, 2006.
• S. Stević, Products of composition and differentiation operators on the weighted Bergman space,'' to appear in Bulletin of the Belgian Mathematical Society---Simon Stevin.
• S. Li and S. Stević, Composition followed by differentiation between Bloch type spaces,'' Journal of Computational Analysis and Applications, vol. 9, no. 2, pp. 195--205, 2007.
• S. Li and S. Stević, Composition followed by differentiation between $H^\infty$ and $\alpha$-Bloch spaces,'' Houston Journal of Mathematics, vol. 35, no. 1, pp. 327--340, 2009.
• S. Li and S. Stević, Composition followed by differentiation from mixed-norm spaces to $\alpha$-Bloch spaces,'' Sbornik Mathematics, vol. 199, no. 12, pp. 1847--1857, 2008.
• S. Stević, Norm and essential norm of composition followed by differentiation from $\alpha$-Bloch spaces to $H_\mu ^\infty$,'' Applied Mathematics and Computation, vol. 207, no. 1, pp. 225--229, 2009.
• S. Stević, Generalized composition operators between mixed-norm and some weighted spaces,'' Numerical Functional Analysis and Optimization, vol. 29, no. 7-8, pp. 959--978, 2008.
• S. Stević, Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces,'' Applied Mathematics and Computation, vol. 211, no. 1, pp. 222--233, 2009.
• X. Zhu, Generalized weighted composition operators from Bloch type spaces to weighted Bergman spaces,'' Indian Journal of Mathematics, vol. 49, no. 2, pp. 139--150, 2007.
• X. Zhu, Products of differentiation, composition and multiplication from Bergman type spaces to Bers type spaces,'' Integral Transforms and Special Functions, vol. 18, no. 3, pp. 223--231, 2007.
• S. Li and S. Stević, Generalized composition operators on Zygmund spaces and Bloch type spaces,'' Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1282--1295, 2008.
• S. Li and S. Stević, Products of composition and integral type operators from $H^\infty$ to the Bloch space,'' Complex Variables and Elliptic Equations, vol. 53, no. 5, pp. 463--474, 2008.
• S. Li and S. Stević, Products of Volterra type operator and composition operator from $H^\infty$ and Bloch spaces to Zygmund spaces,'' Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 40--52, 2008.
• S. Li and S. Stević, Products of integral-type operators and composition operators between Bloch-type spaces,'' Journal of Mathematical Analysis and Applications, vol. 349, no. 2, pp. 596--610, 2009.
• S. Stević, Generalized composition operators from logarithmic Bloch spaces to mixed-norm spaces,'' Utilitas Mathematica, vol. 77, pp. 167--172, 2008.
• S. Stević, On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball,'' Discrete Dynamics in Nature and Society, vol. 2008, Article ID 154263, 14 pages, 2008.
• S. Stević, On a new operator from the logarithmic Bloch space to the Bloch-type space on the unit ball,'' Applied Mathematics and Computation, vol. 206, no. 1, pp. 313--320, 2008.
• S. Stević, On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball,'' Journal of Mathematical Analysis and Applications, vol. 354, no. 2, pp. 426--434, 2009.
• S. Stević, On an integral operator between Bloch-type spaces on the unit ball,'' Bulletin des Sciences Mathématiques. In press.
• S. Stević, Composition operators between $H^\infty$ and $a$-Bloch spaces on the polydisc,'' Zeitschrift für Analysis und ihre Anwendungen, vol. 25, no. 4, pp. 457--466, 2006.
• K. Madigan and A. Matheson, Compact composition operators on the Bloch space,'' Transactions of the American Mathematical Society, vol. 347, no. 7, pp. 2679--2687, 1995.
• K. H. Zhu, Bloch type spaces of analytic functions,'' The Rocky Mountain Journal of Mathematics, vol. 23, no. 3, pp. 1143--1177, 1993.