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Weighted differentiation composition operators from \(H^{\infty }\) and Bloch spaces to \(n\)th weighted-type spaces on the unit disk. (English) Zbl 1195.30073

Summary: We characterize the boundedness and the compactness of weighted differentiation composition operators from the space of bounded analytic functions, the Bloch space, and the little Bloch space to the \(n\)th weighted-type space on the unit disk.

MSC:

30H30 Bloch spaces
30H05 Spaces of bounded analytic functions of one complex variable
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[1] Avetisyan, K. L., Hardy-Bloch type spaces and lacunary series on the polydisk, Glasgow Math. J., 49, 2, 345-356 (2007) · Zbl 1123.32004
[2] Bierstedt, K. D.; Bonet, J.; Taskinen, J., Associated weights and spaces of holomorphic functions, Studia Math., 127, 70-79 (1998)
[3] Bierstedt, K. D.; Summers, W. H., Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. (Series A), 54, 70-79 (1993) · Zbl 0801.46021
[4] Choe, B.; Koo, H.; Smith, W., Composition operators on small spaces, Integral Equations Operator Theory, 56, 357-380 (2006) · Zbl 1114.47028
[6] Cowen, C. C.; MacCluer, B. D., Composition Operators on Spaces of Analytic Functions (1995), CRC Press: CRC Press Boca Raton, FL · Zbl 0873.47017
[7] Hibschwailer, R. A.; Portnoy, N., Composition followed by differentiation between Bergman and Hardy spaces, Rocky Mountain J. Math., 35, 3, 843-855 (2005) · Zbl 1079.47031
[8] Li, S.; Stević, S., Composition followed by differentiation between Bloch type spaces, J. Comput. Anal. Appl., 9, 2, 195-206 (2007) · Zbl 1132.47026
[9] Li, S.; Stević, S., Composition followed by differentiation from mixed norm spaces to \(α\)-Bloch spaces, Mat. Sb., 199, 12, 117-128 (2008) · Zbl 1169.47025
[10] Li, S.; Stević, S., Composition followed by differentiation between \(H^∞\) and \(α\)-Bloch spaces, Houston J. Math., 35, 1, 327-340 (2009) · Zbl 1166.47034
[11] Madigan, K.; Matheson, A., Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., 347, 7, 2679-2687 (1995) · Zbl 0826.47023
[12] Ohno, S., Products of composition and differentiation between Hardy spaces, Bull. Austral. Math. Soc., 73, 2, 235-243 (2006) · Zbl 1102.47015
[13] Stević, S., Composition operators between \(H^∞\) and the \(α\)-Bloch spaces on the polydisc, Z. Anal. Anwendungen, 25, 4, 457-466 (2006) · Zbl 1118.47015
[14] Stević, S., Generalized composition operators from logarithmic Bloch spaces to mixed-norm spaces, Util. Math., 77, 167-172 (2008) · Zbl 1175.47033
[15] Stević, S., Norm of weighted composition operators from Bloch space to \(H_\mu^\infty\) on the unit ball, Ars. Combin., 88, 125-127 (2008) · Zbl 1224.30195
[17] Stević, S., Norm and essential norm of composition followed by differentiation from \(α\)-Bloch spaces to \(H_\mu^\infty \), Appl. Math. Comput., 207, 225-229 (2009) · Zbl 1157.47026
[19] Stević, S., On a new operator from \(H^∞\) to the Bloch-type space on the unit ball, Util. Math., 77, 257-263 (2008) · Zbl 1175.47034
[20] 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) · Zbl 1176.47029
[21] Stević, S., On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball, J. Math. Anal. Appl., 354, 426-434 (2009) · Zbl 1171.47028
[22] Stević, S., Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin, 16, 623-635 (2009) · Zbl 1181.30031
[23] Stević, S., On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces, Nonlinear Anal. TMA, 71, 6323-6342 (2009) · Zbl 1186.47033
[25] Stević, S., On an integral-type operator from logarithmic Bloch-type spaces to mixed-norm spaces on the unit ball, Appl. Math. Comput., 215, 3817-3823 (2010) · Zbl 1184.30052
[26] Ueki, S. I., Composition operators on the Privalov spaces of the unit ball of \(C^n\), J. Korean Math. Soc., 42, 1, 111-127 (2005) · Zbl 1062.32004
[28] Yang, W., On an integral-type operator between Bloch-type spaces, Appl. Math. Comput., 215, 3, 954-960 (2009) · Zbl 1185.45020
[30] Zhu, K., Spaces of Holomorphic Functions in the Unit Ball, Graduate Text in Mathematics 226 (2005), Springer: Springer New York
[31] Zhu, X., Generalized weighted composition operators from Bloch-type spaces to weighted Bergman spaces, Indian J. Math., 49, 2, 139-149 (2007) · Zbl 1130.47017
[32] Zhu, X., Volterra type operators from logarithmic Bloch spaces to Zygmund type space, Inter. J. Modern Math., 3, 3, 327-336 (2008) · Zbl 1169.47027
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