Xu, Likui; Deng, Xiuqin; Liu, Junming A new characterization of weighted composition operators from \(F(p, q, s)\) into Bloch type space. (English) Zbl 1515.47037 Mediterr. J. Math. 18, No. 4, Paper No. 166, 17 p. (2021). Summary: In this paper, we give estimates for the essential norm of a weighted composition operator \(uC_\varphi\) acting on the disk from general function spaces \(F(p, q, s)\) into Bloch-type spaces including \(\alpha\)-Bloch spaces and logarithmic Bloch spaces. MSC: 47B33 Linear composition operators 30H30 Bloch spaces Keywords:Bloch-type spaces; essential norm; weighted composition operator PDFBibTeX XMLCite \textit{L. Xu} et al., Mediterr. J. Math. 18, No. 4, Paper No. 166, 17 p. (2021; Zbl 1515.47037) Full Text: DOI References: [1] Cowen, CC; MacCluer, BD, Composition Operators on Spaces of Analytic Functions (1995), Boca Raton: CRC Press, Boca Raton · Zbl 0873.47017 [2] Hu, Q.; Li, S.; Wulan, H., New essential norm estimates of weighted composition operators from \(H^{\infty }\) into the Bloch space, Complex Var. Elliptic Equ., 62, 5, 600-615 (2017) · Zbl 1364.30062 [3] 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, 1, 51-157 (2012) · Zbl 1252.47026 [4] Hyvärinen, O.; Lindström, M., Estimates of essential norms of weighted composition operators between Bloch-type spaces, J. Math. Anal. Appl., 393, 1, 38-44 (2012) · Zbl 1267.47040 [5] Liang, Y., Integral-type operators from F(p, q, s) space to \(\alpha \)-Bloch-Orlicz and \(\beta \)-Zygmund-Orlicz spaces, Complex Anal. Oper. Theory, 23, 2, 1-26 (2016) [6] Liu, X.; Li, S., Norm and essential norm of a weighted composition operator on the Bloch space, Integral Equ. Oper. Theory, 87, 3, 309-325 (2017) · Zbl 1372.30059 [7] MacCluer, B.; Zhao, R., Essential norms of weighted composition operators between Bloch-type spaces, Rocky Mt. J. Math., 33, 4, 1437-1458 (2003) · Zbl 1061.30023 [8] Montes-Rodríguez, A., Weighted composition operators on weighted Banach spaces of analytic functions, J. Lond. Math. Soc. (2), 61, 3, 872-884 (2000) · Zbl 0959.47016 [9] Ohno, S., Weighted composition operators between \(H^\infty\) and the Bloch space, Taiwan. J. Math., 5, 3, 555-563 (2001) · Zbl 0997.47025 [10] Ohno, S.; Stroethoff, K.; Zhao, R., Weighted composition operators between Bloch-type spaces, Rocky Mt. J. Math., 33, 1, 191-215 (2003) · Zbl 1042.47018 [11] Shapiro, J., Composition Operators and Classical Function Theory (1993), New York: Springer, New York · Zbl 0791.30033 [12] Tjani, M.: Compact composition operators on some Möbius invariant Banach spaces. PhD Dissertation, Michigan State University p. 68 (1996) · Zbl 0963.47023 [13] Ye, S., Weighted composition operators from F(p, q, s) into logarithmic Bloch space, J. Korean Math. Soc., 45, 4, 977-991 (2008) · Zbl 1156.47031 [14] Zhang, X., Boundedness of weighted composition operators on p-Bloch spaces on the unit ball of \(C^n\), J. Math. Study, 36, 3, 243-250 (2003) · Zbl 1053.47021 [15] Zhang, X.; Xiao, J., Weighted composition operator between two analytic function spaces, Adv. Math. (China), 35, 4, 453-462 (2006) · Zbl 1482.30124 [16] Zhao, R.: On a general family of function spaces. Ann. Acad. Sci. Fenn. Math. Diss. 105, 56 (1996) · Zbl 0851.30017 [17] Zhu, K., Bloch type spaces of analytic functions, Rocky Mt. J. Math., 23, 3, 1143-1177 (1993) · Zbl 0787.30019 [18] Zhu, K., Operator Theory in Function Spaces (1990), New York: Marcel Dekker, Inc., New York · Zbl 0706.47019 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.