Document Zbl 1280.47046

Zhou, Ze Hua; Liang, Yu Xia; Zeng, Hong Gang

Essential norms of weighted composition operators from weighted Bergman space to mixed-norm space on the unit ball. (English) Zbl 1280.47046

Acta Math. Sin., Engl. Ser. 29, No. 3, 547-556 (2013).

Authors’ abstract: In this paper, we characterize the boundedness and compactness of weighted composition operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate their essential norms.

Reviewer: Miguel Lacruz (Sevilla)

Cited in 4 Documents

MSC:

47B38	Linear operators on function spaces (general)
32A37	Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
32H02	Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
47G10	Integral operators
47B33	Linear composition operators

Keywords:

weighted composition operator; weighted Bergman space; mixed-norm space; essential norm; compact

Cite Review PDF

Full Text: DOI

References:

[1]	Hu, Z. J.: Extended Cesàro operators on Bergman spaces. J. Math. Anal. Appl., 296, 435–454 (2004) · Zbl 1072.47029 · doi:10.1016/j.jmaa.2004.01.045
[2]	Li, S., Stević, S.: Riemann-Stieltjes operators between different weighted Bergman spaces. Bull. Belg. Math. Soc. Simon Stevin, 15(4), 677–686 (2008) · Zbl 1169.47026
[3]	Stević, S.: On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball. Discrete Dyn. Nat. Soc., 2008, Article ID 154263, 14 pp (2008) · Zbl 1155.32002
[4]	Zhu, K. H.: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, 226, Springer, New York, 2005 · Zbl 1067.32005
[5]	Shields, A. L., Williams, D. L.: Bounded projection, duality, and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc., 162, 287–302 (1971) · Zbl 0227.46034
[6]	Hu, Z. J.: Extended Cesàro operators on mixed norm spaces. Proc. Amer. Math. Soc., 131(7), 2171–2179 (2003) · Zbl 1054.47023 · doi:10.1090/S0002-9939-02-06777-1
[7]	Li, S., Stević, S.: Integral type operators from mixed-norm spaces to {\(\alpha\)}-Bloch spaces. Integr. Transf. Spec. Funct., 18(7), 485–493 (2007) · Zbl 1131.47031 · doi:10.1080/10652460701320703
[8]	Li, S., Stević, S.: Riemann-Stieltjes operators between mixed norm spaces. Indian J. Math., 50(1), 177–188 (2008) · Zbl 1159.47012
[9]	Stević, S.: Integral-type operators from the mixed-norm space to the Bloch-type space on the unit ball. Siberian J. Math., 50(6), 1098–1105 (2009) · Zbl 1217.47069 · doi:10.1007/s11202-009-0121-5
[10]	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 · doi:10.1016/j.na.2009.06.087
[11]	Stević, S.: On operator P {\(\phi\)} g from the logarithmic Bloch-type space to the mixed-norm space on the unit ball. Appl. Math. Comput., 215(12), 4248–4255 (2010) · Zbl 1205.45014 · doi:10.1016/j.amc.2009.12.048
[12]	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 · doi:10.1016/j.amc.2009.11.022
[13]	Zhang, X. J., Xiao, J. B., Hu, Z. J.: The multipliers between the mixed norm spaces in Cn. J. Math. Anal. Appl., 311, 664–674 (2006) · Zbl 1080.32003 · doi:10.1016/j.jmaa.2005.03.010
[14]	Shapiro, J. H.: Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993 · Zbl 0791.30033
[15]	Cowen, C. C., MacCluer, B. D.: Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995 · Zbl 0873.47017
[16]	Zhu, K. H.: Operator Theory in Function Spaces, Marcel Dekker Inc., New York, 1990 · Zbl 0706.47019
[17]	Zhou, Z. H., Chen, R. Y.: Weighted composition operators fom F(p, q, s) to Bloch type spaces. International Jounal of Mathematics, 19(8), 899–926 (2008) · Zbl 1163.47021 · doi:10.1142/S0129167X08004984
[18]	Zhou, Z. H., Liu, Y.: The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications. J. Inequal. Appl., 2006, Article ID 90742, 22pp (2006) · Zbl 1131.47021
[19]	Zhou, Z. H., Shi, J. H.: Compactness of composition operators on the Bloch space in classical bounded symmetric domains. Michigan Math. J., 50, 381–405 (2002) · Zbl 1044.47021 · doi:10.1307/mmj/1028575740
[20]	Zeng, H. G., Zhou, Z. H.: An estimate of the essential norm of a composition operator from F(p, q, s) to B {\(\alpha\)} in the unit ball. J. Inequal. Appl., 2010, Article ID 132970, 22pp (2010) · Zbl 1191.47033
[21]	Ohno, S., Stroethoff, K., Zhao, R.: Weighted composition operators between Bloch-type spaces. Rocky Mountain J. Math., 33(1), 191–215 (2003) · Zbl 1042.47018 · doi:10.1216/rmjm/1181069993
[22]	Ueki, S., Luo, L.: Compact weighted composition operators and multiplication operators between Hardy spaces. Abstr. Appl. Anal., 2008, Article ID 196498, 12 pp (2008) · Zbl 1167.47020
[23]	Ueki, S., Luo, L.: Essential norms of weighted composition operators between weighted Bergman spaces of the ball. Acta Sci. Math., 74, 827–841 (2008) · Zbl 1199.30274
[24]	Stević, S., Ueki, S.: Weighted composition operators from the weighted Bergman space to the weighted Hardy space on the unit ball. Appl. Math. Comput., 215, 3526–3533 (2010) · Zbl 1197.47040 · doi:10.1016/j.amc.2009.10.048
[25]	Rudin, W.: Function Theory in the Unit Ball of C n, Crundlehren Math. Wiss. 241, Springer-Verlag, New York, Berlin, 1980 · Zbl 0495.32001
[26]	Stoll, M.: Invariant Potential Theory in the Unit Ball of C n, Cambridge University Press, Cambridge, 1994 · Zbl 0797.31001

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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.