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Composition operators from the weighted Bergman space to the \(n\)th weighted-type space on the upper half-plane. (English) Zbl 1204.30044

Summary: On the upper half-plane \(\varPi _+ = \{z \in \mathbb C : \text{Im} z > 0\}\), the boundedness of composition operators from weighted Bergman spaces to \(n\)th weighted-type spaces, recently introduced by the author, are characterized.

MSC:

30H10 Hardy spaces
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[1] Choe, B.; Koo, H.; Smith, W., Composition operators on small spaces, Integral Equations Operator Theory, 56, 357-380 (2006) · Zbl 1114.47028
[2] Cowen, C. C.; MacCluer, B. D., Composition Operators on Spaces of Analytic Functions (1995), CRC Press · Zbl 0873.47017
[4] Kang, S. H., Berezin transforms and Toelitz operators on the weighted Bergman spaces of the half-plane, Bull. Korean Math. Soc., 44, 2, 281-290 (2007) · Zbl 1154.47300
[5] Kang, S. H.; Kim, J. Y., The radial derivatives on weighted Bergman spaces, Commun. Korean Math. Soc., 18, 2, 243-249 (2003) · Zbl 1101.30310
[6] Li, S.; Stević, S., Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl., 338, 1282-1295 (2008) · Zbl 1135.47021
[7] Li, S.; Stević, S., Products of Volterra type operator and composition operator from \(H^∞\) and Bloch spaces to the Zygmund space, J. Math. Anal. Appl., 345, 40-52 (2008) · Zbl 1145.47022
[8] Li, S.; Stević, S., Weighted composition operators from Zygmund spaces into Bloch spaces, Appl. Math. Comput., 206, 2, 825-831 (2008) · Zbl 1215.47022
[9] Li, S.; Stević, S., Cesàro type operators on some spaces of analytic functions on the unit ball, Appl. Math. Comput., 208, 378-388 (2009) · Zbl 1166.45009
[10] Sharma, S. D.; Sharma, A. K.; Ahmed, S., Composition operators between Hardy and Bloch-type spaces of the upper half-plane, Bull. Korean Math. Soc., 43, 3, 475-482 (2007) · Zbl 1142.47019
[11] Stević, S., Composition operators between \(H^∞\) and the \(α\)-Bloch spaces on the polydisc, Z. Anal. Anwend., 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
[16] Stević, S., Norms of some operators from Bergman spaces to weighted and Bloch-type space, Util. Math., 76, 59-64 (2008) · Zbl 1160.47027
[19] Stević, S., Norms of some operators on the Bergman and the Hardy space in the unit polydisk and the unit ball, Appl. Math. Comput., 215, 6, 2199-2205 (2009) · Zbl 1186.32004
[20] 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
[21] 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
[22] Stević, S., Weighted composition operators from mixed-norm spaces into weighted Bloch spaces, J. Comput. Anal. Appl., 11, 1, 70-81 (2009) · Zbl 1197.47039
[23] Stević, S., Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball, Appl. Math. Comput., 212, 499-504 (2009) · Zbl 1186.47020
[24] Stević, S., On an integral operator between Bloch-type spaces on the unit ball, Bull. Sci. Math., 134, 329-339 (2010) · Zbl 1189.47032
[25] Stević, S., Weighted differentiation composition operators from \(H^∞\) and Bloch spaces to \(n\) th weigthed-type spaces on the unit disk, Appl. Math. Comput., 216, 3634-3641 (2010) · Zbl 1195.30073
[26] Ueki, S. I., Weighted composition operators on some function spaces of entire functins, Bull. Belg. Math. Soc. Simon Stevin, 17, 2, 343-353 (2010) · Zbl 1191.47032
[28] Zhu, K., Spaces of Holomorphic Functions in the Unit Ball. Spaces of Holomorphic Functions in the Unit Ball, Graduate Text in Mathematics, vol. 226 (2005), Springer: Springer New York · Zbl 1067.32005
[29] Zhu, X., Volterra type operators from logarithmic Bloch spaces to Zygmund type spaces, Int. J. Mod. Math., 3, 3, 327-336 (2008) · Zbl 1169.47027
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