×
Stević, Stevo; Sharma, Ajay K.; Sharma, S. D.

Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the upper half-plane. (English) Zbl 1221.47047

Abstr. Appl. Anal. 2011, Article ID 989625, 10 p. (2011).
Summary: Let \(\psi\) be a holomorphic mapping on the upper half-plane \(\Pi^+ = \{ z \in \mathbb C : \mathfrak I z > 0\}\) and \(\varphi\) be a holomorphic self-map of \(\Pi^+\). We characterize bounded weighted composition operators acting from the weighted Bergman space to the weighted-type space on the upper half-plane. Under a mild condition on \(\psi\), we also characterize the compactness of these operators.

Cited in 4 Documents

MSC:

47B33 Linear composition operators

Keywords:

bounded weighted composition operators; weighted Bergman space; compactness
PDF BibTeX XML Cite
\textit{S. Stević} et al., Abstr. Appl. Anal. 2011, Article ID 989625, 10 p. (2011; Zbl 1221.47047)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] C. C. Cowen and B. D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995. · Zbl 0873.47017
[2] V. Matache, “Composition operators on Hp of the upper half-plane,” Analele Universit\ua\ctii din Timi\csoara, Seria \cStiin\cte Matematice, vol. 27, no. 1, pp. 63-66, 1989. · Zbl 0791.47031
[3] V. Matache, “Composition operators on Hardy spaces of a half-plane,” Proceedings of the American Mathematical Society, vol. 127, no. 5, pp. 1483-1491, 1999. · Zbl 0916.47022
[4] H. J. Schwartz, Composition operators on Hp, Ph.D. thesis, University of Toledo, Ohio, USA, 1969. · Zbl 0193.31104
[5] J. H. Shapiro and W. Smith, “Hardy spaces that support no compact composition operators,” Journal of Functional Analysis, vol. 205, no. 1, pp. 62-89, 2003. · Zbl 1041.46019
[6] A. K. Sharma and S. D. Sharma, “Weighted composition operators between Bergman-type spaces,” Communications of the Korean Mathematical Society, vol. 21, no. 3, pp. 465-474, 2006. · Zbl 1160.47308
[7] S. D. Sharma, A. K. Sharma, and S. Ahmed, “Carleson measures in a vector-valued Bergman space,” Journal of Analysis and Applications, vol. 4, no. 1, pp. 65-76, 2006. · Zbl 1179.30050
[8] S. D. Sharma, A. K. Sharma, and S. Ahmed, “Composition operators between Hardy and Bloch-type spaces of the upper half-plane,” Bulletin of the Korean Mathematical Society, vol. 44, no. 3, pp. 475-482, 2007. · Zbl 1142.47019
[9] S. D. Sharma, A. K. Sharma, and Z. Abbas, “Weighted composition operators on weighted vector-valued Bergman spaces,” Applied Mathematical Sciences, vol. 4, no. 41-44, pp. 2049-2063, 2010. · Zbl 1295.47025
[10] A. L. Shields and D. L. Williams, “Bonded projections, duality, and multipliers in spaces of analytic functions,” Transactions of the American Mathematical Society, vol. 162, pp. 287-302, 1971. · Zbl 0227.46034
[11] R. K. Singh and S. D. Sharma, “Composition operators on a functional Hilbert space,” Bulletin of the Australian Mathematical Society, vol. 20, no. 3, pp. 377-384, 1979. · Zbl 0411.47023
[12] R. K. Singh and S. D. Sharma, “Noncompact composition operators,” Bulletin of the Australian Mathematical Society, vol. 21, no. 1, pp. 125-130, 1980. · Zbl 0411.47024
[13] S. Stević, “Weighted composition operators between mixed norm spaces and H\alpha \infty spaces in the unit ball,” Journal of Inequalities and Applications, Article ID 28629, 9 pages, 2007. · Zbl 1138.47019
[14] S. Stević, “Norm of weighted composition operators from Bloch space to H\mu \infty on the unit ball,” Ars Combinatoria, vol. 88, pp. 125-127, 2008. · Zbl 1224.30195
[15] S. Stević, “Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball,” Applied Mathematics and Computation, vol. 212, no. 2, pp. 499-504, 2009. · Zbl 1186.47020
[16] S. Stević, “Composition operators from the Hardy space to Zygmund-type spaces on the upper half-plane and the unit disc,” Journal of Computational Analysis and Applications, vol. 12, no. 2, pp. 305-312, 2010. · Zbl 1214.47028
[17] S. Stević, “Composition operators from the Hardy space to the n-th weighted-type space on the unit disk and the half-plane,” Applied Mathematics and Computation, vol. 215, no. 11, pp. 3950-3955, 2010. · Zbl 1184.30051
[18] S. Stević, “Composition operators from the weighted Bergman space to the n-th weighted-type space on the upper half-plane,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3379-3384, 2010. · Zbl 1204.30044
[19] S.-I. Ueki, “Hilbert-Schmidt weighted composition operator on the Fock space,” International Journal of Mathematical Analysis, vol. 1, no. 13-16, pp. 769-774, 2007. · Zbl 1160.47306
[20] S.-I. Ueki, “Weighted composition operators on the Bargmann-Fock space,” International Journal of Modern Mathematics, vol. 3, no. 3, pp. 231-243, 2008. · Zbl 1171.47021
[21] S.-I. Ueki, “Weighted composition operators on some function spaces of entire functions,” Bulletin of the Belgian Mathematical Society Simon Stevin, vol. 17, no. 2, pp. 343-353, 2010. · Zbl 1191.47032
[22] X. Zhu, “Weighted composition operators from area Nevanlinna spaces into Bloch spaces,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4340-4346, 2010. · Zbl 1185.30058
[23] F. Forelli, “The isometries of Hpspaces,” Canadian Journal of Mathematics, vol. 16, pp. 721-728, 1964. · Zbl 0132.09403
[24] C. J. Kolaski, “Isometries of weighted Bergman spaces,” Canadian Journal of Mathematics, vol. 34, no. 4, pp. 910-915, 1982. · Zbl 0459.32010
[25] S. Li and S. Stević, “Generalized composition operators on Zygmund spaces and Bloch type spaces,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1282-1295, 2008. · Zbl 1135.47021
[26] S. Stević, “On a new operator from H\infty to the Bloch-type space on the unit ball,” Utilitas Mathematica, vol. 77, pp. 257-263, 2008. · Zbl 1175.47034
[27] S. Stević, “On an integral operator from the Zygmund space to the Bloch-type space on the unit ball,” Glasgow Mathematical Journal, vol. 51, no. 2, pp. 275-287, 2009. · Zbl 1176.47029
[28] S. Stević, “On a new integral-type operator from the Bloch space to Bloch-type spaces on the unit ball,” Journal of Mathematical Analysis and Applications, vol. 354, no. 2, pp. 426-434, 2009. · Zbl 1171.47028
[29] S. Stević, “On an integral operator between Bloch-type spaces on the unit ball,” Bulletin des Sciences Mathématiques, vol. 134, no. 4, pp. 329-339, 2010. · Zbl 1189.47032
[30] X. Zhu, “Generalized weighted composition operators from Bloch type spaces to weighted Bergman spaces,” Indian Journal of Mathematics, vol. 49, no. 2, pp. 139-150, 2007. · Zbl 1130.47017
[31] K. L. Avetisyan, “Integral representations in general weighted Bergman spaces,” Complex Variables, vol. 50, no. 15, pp. 1151-1161, 2005. · Zbl 1089.30037
[32] K. L. Avetisyan, “Hardy-Bloch type spaces and lacunary series on the polydisk,” Glasgow Mathematical Journal, vol. 49, no. 2, pp. 345-356, 2007. · Zbl 1123.32004
[33] K. D. Bierstedt and W. H. Summers, “Biduals of weighted Banach spaces of analytic functions,” Australian Mathematical Society Journal Series A, vol. 54, no. 1, pp. 70-79, 1993. · Zbl 0801.46021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.