Abstract
A new characterization for the boundedness, compactness and the essential norm of generalized weighted composition operators from Bloch-type spaces into Zygmund-type spaces are given in this paper.
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Antòn-Marval, G., Castillo, R., Ramos-Fernández, J.: Maximal functions and properties of the weighted composition operators acting on the Korenblum, \(\alpha \)-Bloch and \(\alpha \)-Zygmund spaces. Cubo 19, 39–51 (2017)
Bonet, J., Domański, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic function. Can. Math. Bull. 42, 139–148 (1999)
Choe, B., Koo, H., Smith, W.: Composition operators on small spaces. Integral Equ. Oper. Theory 56, 357–380 (2006)
Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)
Castillo, R., Marrero-Rodríguez, C., Ramos-Fernández, J.: On a criterion for continuity and compactness of composition operators on the weighted Bloch space. Mediterr. J. Math. 12, 1047–1058 (2015)
García Ortíz, A., Ramos Fernández, J.: Composition operators from logarithmic Bloch spaces to Bloch-type spaces. Georgian Math. J. 20, 671–686 (2013)
Hyvärinen, O., Kemppainen, M., Lindström, M., Rautio, A., Saukko, E.: The essential norm of weighted composition operators on weighted Banach spaces of analytic functions. Integral Equ. Oper. Theory 72, 151–157 (2012)
Hibschweiler, R., Portnoy, N.: Composition followed by differentiation between Bergman and Hardy spaces. Rocky Mt. J. Math. 35, 843–855 (2005)
Hu, Q., Shi, Y., Shi, Y., Zhu, X.: Essential norm of generalized weighted composition operators from the Bloch space into the Zygmund space. J. Inequalities Appl. 2016, 123 (2016)
Li, H., Fu, X.: A new characterization of generalized weighted composition operators from the Bloch space into the Zygmund space. J. Funct. Spaces Appl. 2013, 12 (2013). Article ID 925901
Li, S., Stević, S.: Volterra type operators on Zygmund space. J. Inequalities Appl. 2007, 032124 (2007). Article ID 32124
Li, S., Stević, S.: Composition followed by differentiation between Bloch type spaces. J. Comput. Anal. Appl. 9, 195–205 (2007)
Li, S., Stević, S.: Weighted composition operators from Bergman-type spaces into Bloch spaces. Proc. Indian Acad. Sci. Math. Sci. 117(3), 371–385 (2007)
Li, S., Stević, S.: Generalized composition operators on Zygmund spaces and Bloch type spaces. J. Math. Anal. Appl. 338, 1282–1295 (2008)
Li, S., Stević, S.: Weighted composition operators from Zygmund spaces into Bloch spaces. Appl. Math. Comput. 206, 825–831 (2008)
Li, S., Stević, S.: Composition followed by differentiation from mixed-norm spaces to \(\alpha \)-Bloch spaces. Sb. Math. 199(12), 1847–1857 (2008)
Li, S., Stević, S.: Composition followed by differentiation between \(H^\infty \) and \(\alpha \)-Bloch spaces. Houst. J. Math. 35, 327–340 (2009)
Li, S., Stević, S.: Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces. Appl. Math. Comput. 217, 3144–3154 (2010)
Li, S., Stević, S.: Generalized weighted composition operators from \(\alpha \)-Bloch spaces into weighted-type spaces. J. Inequalities Appl. 2015, 337 (2015). Article No. 265
Liang, Y., Zhou, Z.: Essential norm of the product of differentiation and composition operators between Bloch-type space. Arch. Math. 100, 347–360 (2013)
Malavé, M., Ramos Fernández, J.: The associated weight and the essential norm of weighted composition operators. Banach J. Math. Anal. 9, 144–158 (2015)
MacCluer, B., Zhao, R.: Essential norm of weighted composition operators between Bloch-type spaces. Rocky Mt. J. Math. 33, 1437–1458 (2003)
Madigan, K., Matheson, A.: Compact composition operators on the Bloch space. Trans. Am. Math. Soc. 347, 2679–2687 (1995)
Montes-Rodriguez, A.: The essential norm of composition operators on the Bloch space. Pac. J. Math. 188, 339–351 (1999)
Ohno, S., Stroethoff, K., Zhao, R.: Weighted composition operators between Bloch-type spaces. Rocky Mt. J. Math. 33, 191–215 (2003)
Ramos Fernández, J.: An estimation for the essential norm of composition operators acting on Bloch-type spaces. Int. J. Math. 24, 1350104 (2013). Article ID 1350104
Ramos Fernández, J.: Logarithmic Bloch spaces and their weighted composition operators. Rend. Circ. Mat. Palermo 65, 159–174 (2016)
Stević, S.: Norm and essential norm of composition followed by differentiation from \(\alpha \)-Bloch spaces to \(H^\infty _\mu \). Appl. Math. Comput. 207, 225–229 (2009)
Stević, S.: Products of composition and differentiation operators on the weighted Bergman space. Bull. Belg. Math. Soc. Simon Stevin 16, 623–635 (2009)
Stević, S.: On an integral operator from the Zygmund space to the Bloch-type space on the unit ball. Glasg. J. Math. 51, 275–287 (2009)
Stević, S.: On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball. Abstr. Appl. Anal. 2010, 7 (2010). Article ID 198608
Stević, S.: Weighted differentiation composition operators from mixed-norm spaces to the \(n\)th weighted-type space on the unit disk. Abstr. Appl. Anal. 2010, 222–233 (2010). Article ID 246287
Stević, S.: Weighted differentiation composition operators from \(H^\infty \) and Bloch spaces to \(n\)th weigthed-type spaces on the unit disk. Appl. Math. Comput. 216, 3634–3641 (2010)
Stević, S.: Characterizations of composition followed by differentiation between Bloch-type spaces. Appl. Math. Comput. 218, 4312–4316 (2011)
Stević, S., Sharma, A.K., Bhat, A.: Products of multiplication composition and differentiation operators on weighted Bergman spaces. Appl. Math. Comput. 217, 8115–8125 (2011)
Tjani, M.: Compact composition operators on some Möbius invariant Banach space. Ph.D. dissertation, Michigan State University (1996)
Wu, Y., Wulan, H.: Products of differentiation and composition operators on the Bloch space. Collet. Math. 63, 93–107 (2012)
Wulan, H., Zheng, D., Zhu, K.: Compact composition operators on BMOA and the Bloch space. Proc. Am. Math. Soc. 137, 3861–3868 (2009)
Yang, W., Zhu, X.: Generalized weighted composition operators from area Nevanlinna spaces to Bloch-type spaces. Taiwan. J. Math. 16, 869–883 (2012)
Yu, Y., Liu, Y.: Weighted differentiation composition operators from \(H^\infty \) to Zygmund spaces. Integ. Transform. Spec. Funct. 22, 507–520 (2011)
Zhao, R.: Essential norms of composition operators between Bloch type spaces. Proc. Am. Math. Soc. 138, 2537–2546 (2010)
Zhu, K.: Operator Theory in Function Spaces, 2nd edn. Amer. Math. Soc, Providence (2007)
Zhu, X.: Generalized weighted composition operators on Bloch-type spaces. J. Inequalities Appl. 2015, 59–68 (2015)
Zhu, X.: Essential norm of generalized weighted composition operators on Bloch-type spaces. Appl. Math. Comput. 274, 133–142 (2016)
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Communicated by See Keong Lee.
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Hu, Q. Generalized Weighted Composition Operators from Bloch-Type Spaces into Zygmund-Type Spaces. Bull. Malays. Math. Sci. Soc. 42, 2381–2394 (2019). https://doi.org/10.1007/s40840-018-0605-1
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DOI: https://doi.org/10.1007/s40840-018-0605-1