Composition operators from Zygmund spaces into Besov Zygmund-type spaces‎

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran

Abstract

‎In this paper first‎, ‎the boundedness and compactness of a composition operator from Zygmund space to Besov Zygmund-type space are studied‎. ‎Then we study this concepts for this operator by using the hyperbolic-type analytic Besov Zygmund-type class‎. ‎Finally‎, ‎we show the relation between the hyperbolic-type analytic Besov Zygmund-type class and the meromorphic (or spherical) Besov Zygmund-type class‎.

Keywords

Main Subjects


[1] E. Abbasi and H. Vaezi, Generalized weighted composition operators from the Bloch-type spaces to the weighted Zygmund spaces, Filomat, 33 (2019), pp. 981–992.
[2] F. Colonna and S. Li, Weighted composition operators from H∞ into the Zygmund spaces, Complex Anal. Oper. Theory, 7 (2013), pp. 1495–1512.
[3] , Weighted composition operators from the bloch space and the analytic besov spaces into the zygmund space, Journal of Operators, 2013 (2013), p. 154029.
[4] , Weighted composition operators from the Lipschitz space into the Zygmund space, Math. Inequal. Appl., 17 (2014), pp. 963–975.
[5] F. Colonna and M. Tjani, Weighted composition operators from the Besov spaces into the weighted-type space H∞ µ , J. Math. Anal. Appl., 402 (2013), pp. 594–611.
[6] J. Du, S. Li, and Y. Zhang, Essential norm of generalized composition operators on Zygmund type spaces and Bloch type spaces, Ann. Polon. Math., 119 (2017), pp. 107–119.
[7] P. L. Duren, Theory of Hp spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York[1]London, 1970.
[8] Q. Hu, S. Li, and Y. Zhang, Essential norm of weighted composition operators from analytic Besov spaces into Zygmund type spaces, J. Contemp. Mathemat. Anal., 54 (2019), pp. 129–142.
[9] H. Li and Z. Guo, On a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces, J. Inequal. Appl., (2015), pp. 2015:132, 18.
[10] A. H. Sanatpour and M. Hassanlou, Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces, Filomat, 31 (2017), pp. 2877–2889.
[11] S. Stevic´, Composition operators from the Hardy space to Zygmund-type spaces on the upper half-plane and the unit disc, J. Comput. Anal. Appl., 12 (2010), pp. 305–312.
[12] S. Ye and Q. Hu, Weighted composition operators on the Zygmund space, Abstr. Appl. Anal., (2012), pp. Art. ID 462482, 18.
[13] X. Zhu, Integral-type operators from iterated logarithmic Bloch spaces to Zygmund-type spaces, Appl. Math. Comput., 215 (2009), pp. 1170–1175.