Document Type : Research Paper
Author
Engineering Faculty of Khoy, Urmia University, Urmia, Iran.
Abstract
Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.
Keywords
[1] J. Bonet, M. Lindstrom, and E. Wolf, Differences of Composition operators between weighted Banach spaces of holomorphic functions, J. Aust. Math. Soc., 84 (2008), pp. 9-20.
[2] C.C. Cowen and B.D. Maccluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995.
[3] J. Dai and C. Ouyang, Differences of weighted composition cperators on H∞α (BN), J. Ineq. Appl., 2009 (2009), pp. 1-20.
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[5] T. Hosokawa and S. Ohnol, Differences of weighted composition operators acting from Bloch space to $H^1$, Tran. Amer. Math. Soc., 363 (2011), pp. 5321-5340.
[6] S. Li, Differences of generalized composition operators on the Bloch space, J. Math. Anal. Appl., 394 (2012), pp. 706-711.
[7] S. Li and S. Stevic, Generalized weighted composition operators from a-Bloch spaces into weighted-type spaces, J. Inequal. Appl., 2015:265 (2015), pp. 1-12.
[8] H. Li and X. Fua, New characterization of generalized weighted composition operators from the bloch space into the zygmund space, J. Funct. Spaces Appl., 2013 (2013), 6 pages.
[9] X. Liu and S. Li, Differences of generalized weighted composition operators from the bloch space into bers-type spaces, Filomati, 31 (2017), pp. 1671-1680.
[10] B. MacCluer, S. Ohno and R. Zhao, Topological structure of the space of composition operators on $H^1$, Integ. Equ. Operator Theory, 40 (2001), pp. 481-494.
[11] J. Moorhouse, Compact differences of composition operators, J. Funct. Anal., 219 (2008), pp. 70-92.
[12] P. Nieminen, Compact differences of composition operators on Bloch and lipschitz spaces, Comput. Methods Funct. Theory, 7 (2007), pp. 325-344.
[13] J.H. Shapiro, Composition operator and classical function theory, Springer, New York, 1993.
[14] E. Wolf, Compact differences of composition operators, Bull. Austral. Math. Soc., 77 (2008), pp. 161-165.
[15] W. Yang and X. Zhu, Differences of generalized weighted composition operators between growth spaces, Annales Polonici Mathematici, 112 (2014), 67-83.
[16] K. Yang and Z. Zhou, Essential norm of the difference of composition operators on bloch space, Czechoslovak Math. J., 60 (2010), pp. 1139-1152.
[17] X. Zhu, Generalized weighted composition operators on Bloch-type spaces, J. Inequal. Appl., 2015:59 (2015).
[18] X. Zhu, Essential norm of generalized weighted composition operators on Bloch-type spaces, Appl. Math. Comput., 274 (2016), pp. 133-142.
[19] K. Zhu, Boch type spaces of analytic functions, Rocky Mountain J. Math., 23 (1993), pp. 1143-1177.
[20] K. Zhu, Spaces of holomorphic functions in the unit Ball. Springer, New York, 2005.
[2] C.C. Cowen and B.D. Maccluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995.
[3] J. Dai and C. Ouyang, Differences of weighted composition cperators on H∞α (BN), J. Ineq. Appl., 2009 (2009), pp. 1-20.
[4] T. Hosokawa and S. Ohno, Differences of composition operators on the Bloch spaces, J. Operator Theory, 57 (2), (2007), pp. 229-242.
[5] T. Hosokawa and S. Ohnol, Differences of weighted composition operators acting from Bloch space to $H^1$, Tran. Amer. Math. Soc., 363 (2011), pp. 5321-5340.
[6] S. Li, Differences of generalized composition operators on the Bloch space, J. Math. Anal. Appl., 394 (2012), pp. 706-711.
[7] S. Li and S. Stevic, Generalized weighted composition operators from a-Bloch spaces into weighted-type spaces, J. Inequal. Appl., 2015:265 (2015), pp. 1-12.
[8] H. Li and X. Fua, New characterization of generalized weighted composition operators from the bloch space into the zygmund space, J. Funct. Spaces Appl., 2013 (2013), 6 pages.
[9] X. Liu and S. Li, Differences of generalized weighted composition operators from the bloch space into bers-type spaces, Filomati, 31 (2017), pp. 1671-1680.
[10] B. MacCluer, S. Ohno and R. Zhao, Topological structure of the space of composition operators on $H^1$, Integ. Equ. Operator Theory, 40 (2001), pp. 481-494.
[11] J. Moorhouse, Compact differences of composition operators, J. Funct. Anal., 219 (2008), pp. 70-92.
[12] P. Nieminen, Compact differences of composition operators on Bloch and lipschitz spaces, Comput. Methods Funct. Theory, 7 (2007), pp. 325-344.
[13] J.H. Shapiro, Composition operator and classical function theory, Springer, New York, 1993.
[14] E. Wolf, Compact differences of composition operators, Bull. Austral. Math. Soc., 77 (2008), pp. 161-165.
[15] W. Yang and X. Zhu, Differences of generalized weighted composition operators between growth spaces, Annales Polonici Mathematici, 112 (2014), 67-83.
[16] K. Yang and Z. Zhou, Essential norm of the difference of composition operators on bloch space, Czechoslovak Math. J., 60 (2010), pp. 1139-1152.
[17] X. Zhu, Generalized weighted composition operators on Bloch-type spaces, J. Inequal. Appl., 2015:59 (2015).
[18] X. Zhu, Essential norm of generalized weighted composition operators on Bloch-type spaces, Appl. Math. Comput., 274 (2016), pp. 133-142.
[19] K. Zhu, Boch type spaces of analytic functions, Rocky Mountain J. Math., 23 (1993), pp. 1143-1177.
[20] K. Zhu, Spaces of holomorphic functions in the unit Ball. Springer, New York, 2005.
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