Share This Article:

Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains

Abstract Full-Text HTML XML Download Download as PDF (Size:433KB) PP. 649-664
DOI: 10.4236/apm.2014.412074    2,853 Downloads   3,198 Views   Citations

ABSTRACT

In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for
to be compact.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Su, J. , Li, H. , Miao, X. and Wang, R. (2014) Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains. Advances in Pure Mathematics, 4, 649-664. doi: 10.4236/apm.2014.412074.

References

[1] Ramos-Fernández, J. C. (2011) Composition Operators between μ-Bloch Spaces. Extracta Mathematicae, 26, 75-88.
[2] Wolf, E. (2011) Weighted Composition Operators between Weighted Bloch Type Spaces. Bulletin de la Société Royale des Sciences de Liège, 80, 806-816.
[3] Dai, J.N. (2012) Compact Composition Operators on the Bloch Space of the Unit Ball. Journal of Mathematical Analysis and Applications, 386, 294-299. http://dx.doi.org/10.1016/j.jmaa.2011.07.067
[4] Li, J.F. (2010) Composition Operators from p-Bloch Spaces to Little q-Bloch Spaces on the Unit Ball of Cn. Acta Mathematica Sinica (Series B), 30, 1013-1020.
[5] Zhang, M.Z. and Xu, W. (2007) Composition Operators on α-Bloch Spaces of the Unit Ball. Acta Mathematica Sinica (Series B), 23, 1991-2002.
[6] Zhang, X.J. and Li, J.X. (2009) Weighted Composition Operators Between μ-Bloch Spaces over the Unit Ball of Cn. (Chinese). Acta Mathematica Sinica (Series A), 29, 573-583.
[7] Zhou, Z.H. and Zeng, H.G. (2003) Composition Operators between p-Bloch Space and q-Bloch Space in the Unit Ball. Progr. Progress in Natural Science (Engl. Ed.), 13, 233-236.
[8] Stevo, S. (2008) Norm of Weighted Composition Operators from Bloch Space to on the Unit Ball. Ars Combinatoria, 88, 125-127.
[9] Tang, X.M. and Zhang, R.J. (2013) Weighted Composition Operator from Bloch-Type Space to H∞ Space on the Unit Ball. Mathematical Inequalities and Applications, 16, 289-299. http://dx.doi.org/10.7153/mia-16-22
[10] Li, S.X. and Zhu, X.L. (2004) Essential Norm of Weighted Composition Operator between α-Bloch Space and β-Bloch Space in Polydiscs. International Journal of Mathematics and Mathematical Sciences, 69-72, 3941-3950.
[11] Zhou, Z.H. and Shi, J.H. (2001) Compact Composition Operators on the Bloch Space in Polydiscs. Science in China Series A, 44, 286-291. http://dx.doi.org/10.1007/BF02878708
[12] Zhou, Z.H. and Wei, Z.Q. (2005) Weighted Composition Operators on the Bloch Space in Polydiscs (Chinese). Journal of Mathematics (Wuhan University), 25, 435-440.
[13] Allen, R.F. and Colonna, F. (2010) Weighted Composition Operators on the Bloch Space of a Bounded Homogeneous Domain. In: Operator Theory: Advances and Applications, Volume 1. Operators, Matrices and Analytic Functions, Oper. Theory Adv. Appl., 202, Birkh?user Verlag, Basel, 11-37.
[14] Allen, R.F. and Colonna, F. (2009) Multiplication Operators on the Bloch Space of Bounded Homogeneous Domains. Computational Methods and Function Theory, 9, 679-693. http://dx.doi.org/10.1007/BF03321751
[15] Deng, F.W. and Ouyang, C.H. (2006) Bloch Spaces on Bounded Symmetric Domains in Complex Banach Spaces. Science in China Series A, 49, 1625-1632. http://dx.doi.org/10.1007/s11425-006-2050-0
[16] Shi, J.H. and Luo, L. (2001) Composition Operators on the Bloch Space of Several Complex Variables (Chinese). Acta Mathematica Sinica (Chinese Series), 44, 1-10.
[17] Timony, R.M. (1980) Bloch Functions in Several Complex Variables, I. Bulletin of the London Mathematical Society, 12, 241-267. http://dx.doi.org/10.1112/blms/12.4.241
[18] Zhou, Z.H. and Shi, J.H. (2002) Compactness of Composition Operators on the Bloch Space in Classical Bounded Symmetric Domains. Michigan Mathematical Journal, 50, 381-405.
http://dx.doi.org/10.1307/mmj/1028575740
[19] Lu, Q.K. (1963) The Classical Manifolds and the Classical Domains (Chinese). Shanghai Scientific and Technical Publishers, Shanghai.
[20] Pan, W.Q. (2012) Composition Operators between p-Bloch Space and q-Bloch Space in the First Classical Bounded Symmetric Domain. Master’s Thesis, Jiangsu Normal University, Xuzhou.
[21] Kuang, J.C. (2004) Applied Inequalities (Chinese). 3nd Edition, Shandong Science and Technology Press, Shandong.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.