Liang, Yu-Xia; Zhou, Ze-Hua The products of differentiation and composition operators from logarithmic Bloch spaces to \(\mu \)-Bloch spaces. (English) Zbl 1508.47087 Bull. Iran. Math. Soc. 46, No. 1, 159-176 (2020). Summary: In this paper, we present the new characterizations, in terms of the sequence \(\{z^j\}_{j=1}^\infty \), about the boundedness and essential norm estimation for the products of differentiation and composition operators from logarithmic Bloch spaces to \(\mu \)-Bloch spaces on the unit disk. Then our main results are applied to show the boundedness of a non-trivial product operator \(C_\varphi D^m\) with \(\varphi (z)=z^2\). Cited in 4 Documents MSC: 47B91 Operators on complex function spaces 30H30 Bloch spaces 47B33 Linear composition operators Keywords:differentiation; essential norm; composition operator; Bloch space PDFBibTeX XMLCite \textit{Y.-X. Liang} and \textit{Z.-H. Zhou}, Bull. Iran. Math. Soc. 46, No. 1, 159--176 (2020; Zbl 1508.47087) Full Text: DOI References: [1] Castillo, Re; Clahane, Dd; López, Jf Farías; Ramos-Fernández, Jc, Composition operators from logarithmic Bloch spaces to weighted Bloch spaces, Appl. Math. Comp., 219, 6692-6706 (2013) · Zbl 1304.47030 [2] Contreras, Md; Hernández-Díaz, Ag, Weighted composition operators in weighted Banach spaces of analytic functions, J. Aust. Math. Soc. Ser. A, 69, 41-60 (2000) · Zbl 0990.47018 [3] Cowen, Cc; Maccluer, Bd, Composition Operators on Spaces of Analytic Functions (1995), Boca Raton: CRC Press, Boca Raton [4] Hyvärinen, O.; Lindström, M., Estimates of essential norms of weighted composition operators between Bloch-type spaces, J. Math. Anal. Appl., 393, 38-44 (2012) · Zbl 1267.47040 [5] 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 Eq. Oper. Theory, 72, 151-157 (2012) · Zbl 1252.47026 [6] Liang, Yx; Chen, C., New characterizations for differences of Volterra-type operators from \(\alpha \)-weighted-type space to \(\beta \)-Bloch-Orlicz space, Math. Nachr., 291, 14-15, 2298-2317 (2018) · Zbl 06986915 [7] Liang, Yx; Zhou, Zh, Essential norm of the product of differentiation and composition operators between Bloch-type spaces, Arch. Math., 100, 347-360 (2013) · Zbl 1276.47041 [8] Liang, Yx; Zhou, Zh, New estimate of the essential norm of composition followed by differentiation between Bloch-type spaces, Banach J. Math. Anal., 8, 118-137 (2014) · Zbl 1323.47041 [9] Liang, Yx; Zhou, Zh, Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch-type spaces, Math. Nachr., 290, 2-3, 349-366 (2017) · Zbl 1370.47040 [10] Gorkin, P.; Maccluer, Bd, Essential norms of composition operators, Integral Eq. Oper. Theory, 48, 27-40 (2004) · Zbl 1065.47027 [11] Maccluer, B.; Zhao, R., Essential norms of weighted composition operators between Bloch-type spaces, Rocky Mt J. Math., 33, 1437-1458 (2003) · Zbl 1061.30023 [12] Shapiro, Jh, Composition Operators and Classical Function Theory (1993), New York: Springer, New York [13] Wu, Y.; Wulan, H., Products of differentiation and composition operators on the Bloch space, Collect. Math., 63, 93-107 (2012) · Zbl 1267.30087 [14] Wulan, H.; Zheng, D.; Zhu, K., Compact composition operators on \(BMOA\) and the Bloch space, Proc. Am. Math. Soc., 137, 3861-3868 (2009) · Zbl 1194.47038 [15] Zhao, Rh, Essential norms of composisition operators between Bloch type spaces, Proc. Am. Math. Soc., 138, 2537-2546 (2010) · Zbl 1190.47028 [16] Zhu, Kh, Operator Theory in Function Spaces (1990), New York: Marcel Dekker, New York [17] Zeng, Hg; Zhou, Zh, Essential norm estimate of a composition operator between Bloch-type spaces in the unit ball, Rocky Mt J. Math., 42, 3, 1049-1071 (2012) · Zbl 1268.47035 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.