## New characterizations for the essential norms of generalized weighted composition operators between Zygmund-type spaces.(English)Zbl 1474.30269

Summary: We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund-type spaces. Consequently, we obtain new characterizations for the compactness of such operators.

### MSC:

 30H40 Zygmund spaces 47B33 Linear composition operators
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### References:

 [1] Duren, P. L., Theory of H^p spaces (1970), New York, USA: Academic Press, New York, USA · Zbl 0215.20203 [2] Hu, Q., Generalized weighted composition operators from Bloch-type spaces into Zygmund-type spaces, Bulletin of the Malaysian Mathematical Sciences Society, 42, 5, 2381-2394 (2019) · Zbl 1425.30044 [3] Hu, Q.; Shi, Y.; Shi, Y.; Zhu, X., Essential norm of generalized weighted composition operators from the Bloch space to the Zygmund space, Journal of Inequalities and Applications, 2016, 1 (2016) · Zbl 1337.30066 [4] 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 Equations and Operator Theory, 72, 2, 151-157 (2012) · Zbl 1252.47026 [5] Hyvärinen, O.; Lindström, M., Estimates of essential norms of weighted composition operators between Bloch- type spaces, Journal of Mathematical Analysis and Applications, 393, 1, 38-44 (2012) · Zbl 1267.47040 [6] Sanatpour, A. H.; Hassanlou, M., Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces, Univerzitet u Nišu, 31, 2877-2889 (2017) [7] Zhu, X., Essential norm of generalized weighted composition operators on Bloch-type spaces, Applied Mathematics and Computation, 274, 133-142 (2016) · Zbl 1410.30032 [8] Montes-Rodríguez, A., Weighted composition operators on weighted Banach spaces of analytic functions, Journal of the London Mathematical Society, 61, 872-884 (2008) · Zbl 0959.47016 [9] Sanatpour, A. H.; Hassanlou, M., Essential norms of weighted composition operators between Zygmund-type spaces and Bloch-type spaces, Turkish Journal of Mathematics, 38, 872-882 (2014) · Zbl 1325.47058 [10] Liu, Y.; Yu, Y., Composition followed by differentiation between H^∞ and Zygmund spaces, Complex Analysis and Operator Theory, 6, 121-137 (2012) · Zbl 1275.47072 [11] Long, J.; Qiu, C.; Wu, P., Weighted composition followed and proceeded by differentiation operators from Zygmund spaces to Bloch-type spaces, Journal of Inequalities and Applications, 2014 (2014) · Zbl 1310.47051 [12] Li, H.; Fu, X., New characterization of generalized weighted composition operators from the Bloch space into the Zygmund space, Journal of Function Spaces and Applications, 2013, article 925901, 1-6 (2013) · Zbl 1383.47003 [13] Li, S.; Stević, S., Generalized weighted composition operators from α-Bloch spaces into weighted-type spaces, Journal of Inequalities and Applications, 2015, 1 (2015) · Zbl 1338.47018 [14] Zhu, X., Generalized weighted composition operators from Bloch spaces into Bers-type spaces, Univerzitet u Nišu, 26, 1163-1169 (2012) · Zbl 06451330 [15] Stević, S., Weighted differentiation composition operators from the mixed-norm space to the n-th weigthed-type space on the unit disk, Abstract and Applied Analysis, 2010 (2010) · Zbl 1198.30014 [16] Zhu, X., Generalized weighted composition operators on Bloch-type spaces, Journal of Inequalities and Applications, 2015 (2015) · Zbl 1309.47027 [17] Stević, S., Essential norm of some extensions of the generalized composition operators between k-th weighted-type spaces, Journal of Inequalities and Applications, 2017 (2017) · Zbl 06775985 [18] Zhu, K., Bloch type spaces of analytic functions, The Rocky Mountain Journal of Mathematics, 23, 1143-1177 (1993) · Zbl 0787.30019 [19] Zhao, R., Essential norms of composition operators between Bloch type spaces, Proceedings of the American Mathematical Society, 138, 2537-2546 (2010) · Zbl 1190.47028 [20] Cowen, C. C.; Maccluer, B. D., Composition Operators on Spaces of Analytic Functions (1995), Boca Raton: CRC Press, Boca Raton · Zbl 0873.47017
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