Abstract
Some characterizations for the boundedness, compactness and essential norm of a class of product-type operators \(T^n_{u,v,\varphi }\) from the Bloch space and little Bloch space into Zygmund-type spaces are given in this paper.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Abbasi, E., Vaezi, H.: Generalized weighted composition operators from the Bloch-type spaces to the weighted Zygmund spaces. Filomat 33, 981–992 (2019)
Cowen, C.C., MacCluer, B.D.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)
Du, J., Li, S., Zhang, Y.: Essential norm of generalized composition operators on Zygmund type spaces and Bloch type spaces. Ann. Polon. Math. 119, 107–119 (2017)
Du, J., Li, S., Zhang, Y.: Essential norm of weighted composition operators on Zygmund-type spaces with normal weight. Math. Inequal. Appl. 21, 701–714 (2018)
Hu, Q., Li, S., Zhang, Y.: Essential norm of weighted composition operators from analytic Besov spaces into Zygmund type spaces. J. Contemp. Math. Anal. 54(3), 129–142 (2019)
Jiang, Z.: Product-type operators from Zygmund spaces to Bloch–Orlicz spaces. Complex Var. Elliptic Equ. 62, 1645–1664 (2017)
Li, H., Fu, X.: A new characterization of generalized weighted composition operators from the Bloch space into the Zygmund space. J. Funct. Spaces Appl. (2013) (article ID 925901)
Li, S., Stević, S.: Volterra type operators on Zygmund spaces. J. Inequal. Appl. (2007) (article ID 32124)
Li, S., Stević, S.: Weighted composition operators from Zygmund spaces into Bloch spaces. Appl. Math. Comput. 206, 825–831 (2008)
Li, S., Stević, S.: Generalized weighted composition operators from \(\alpha \)-Bloch spaces into weighted-type spaces. J. Inequal. Appl. 2015, 265 (2015)
Liu, Y., Yu, Y.: Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball. J. Math. Anal. Appl. 423, 76–93 (2015)
Liu, Y., Yu, Y.: The product-type operators from logarithmic Bloch spaces to Zygmund-type spaces. Filomat 33, 3639–3653 (2019)
MacCluer, B.D., Zhao, R.: Essential norms of weighted composition operators between Bloch-type spaces. Rocky Mt. J. Math. 33, 1437–1458 (2003)
Madigan, K., Matheson, A.: Compact composition operators on the Bloch spaces. Trans. Am. Math. Soc. 347, 2679–2687 (1995)
Stević, S.: Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces. Appl. Math. Comput. 211, 222–233 (2009)
Stević, S.: Weighted differentiation composition operators from the mixed-norm space to the nth weighted-type space on the unit disk. Abstr. Appl. Anal. (2010) (article ID 246287)
Stević, S.: Weighted differentiation composition operators from \(H^\infty \) and Bloch spaces to nth weighted-type spaces on the unit disk. Appl. Math. Comput. 216, 3634–3641 (2010)
Stević, S., Sharma, A.: On a product-type operator between Hardy and \(\alpha \)-Bloch spaces of the upper half-plane. J. Inequal. Appl. 2018, 273 (2018)
Stević, S., Sharma, A., Bhat, A.: Products of multiplication composition and differentiation operators on weighted Bergman spaces. Appl. Math. Comput. 217, 8115–8125 (2011)
Stević, S., Sharma, A., Bhat, A.: Essential norm of products of multiplications composition and differentiation operators on weighted Bergman spaces. Appl. Math. Comput. 218, 2379–2386 (2011)
Stević, S., Sharma, A., Krishan, R.: Boundedness and compactness of a new product-type operator from general space to Bloch-type spaces. J. Inequal. Appl. 2016, 219 (2016)
Tjani, M.: Compact composition operators on some Möbius invariant Banach space. Ph.D. dissertation, Michigan State university (1996)
Zhu, K.: Bloch type spaces of analytic functions. Rocky Mt. J. Math. 23, 1143–1177 (1993)
Zhu, K.: Operator Theory in Function Spaces, Mathematical Surveys and Monographs, vol. 138, 2nd edn. American Mathematical Society, Providence (2007)
Zhu, X.: Products of differentiation, composition and multiplication from Bergman type spaces to Bers type space. Integr. Transform. Spec. Funct. 18, 223–231 (2007)
Zhu, X.: Generalized weighted composition operators on weighted Bergman spaces. Numer. Funct. Anal. Opt. 30, 881–893 (2009)
Zhu, X.: Generalized weighted composition operators from Bloch spaces into Bers-type spaces. Filomat 26, 1163–1169 (2012)
Zhu, X.: Generalized weighted composition operators on Bloch-type spaces. J. Inequal. Appl. 2015, 59–68 (2015)
Zhu, X.: Essential norm of generalized weighted composition operators on Bloch-type spaces. Appl. Math. Comput. 274, 133–142 (2016)
Zhu, X.: Generalized weighted composition operators on weighted Bergman spaces, II. Math. Inequal. Appl. 22, 1055–1066 (2019)
Zhu, X., Abbasi, E., Ebrahimi, A.: A class of operators related composition operators from the Besov spaces into the Bloch space. Bull. Iran. Math. Soc. (2020). https://doi.org/10.1007/s41980-020-00374-w
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Mohammad B. Asadi.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abbasi, E., Zhu, X. Product-Type Operators from the Bloch Space into Zygmund-Type Spaces. Bull. Iran. Math. Soc. 48, 385–400 (2022). https://doi.org/10.1007/s41980-020-00523-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41980-020-00523-1