On F(p,q,s) Spaces and Weighted Differentiation Composition Operators on them
Download PDF
Authors: M. SAFARZADEH, M. HASSANLOU, M. ETEFAGH AND Z. Z. CHARANDABI
DOI: 10.46793/KgJMat2609.1433S
Abstract:
In this work, we first consider weighted differentiation composition operator from a general family of analytic functions into Bloch–type space and find an approximation for the essential norm. Then, we characterize the boundedness of the operator into Zygmund–type space and finally, essential norm of this operator is estimated.
Keywords:
Boundedness, compactness, essential norm, Zygmund type space.
References:
[1] S. Alyusof and N. Hmidouch, Essential norm of t-generalized composition operators from F(p,q,s) to iterated weighted-type Banach space, Mathematics 12 (2024), Article ID 1320. https://doi.org/10.3390/math12091320
[2] Z. Guo, Stević–Sharma operator from QK(p,q) space to Zygmund-type space, Filomat 36(19) (2022), 6805–6820. https://doi.org/10.2298/FIL2219805G
[3] H. Li and Z. Guo, Weighted composition operators from F(p,q,s) spaces to nth weighted-Orlicz spaces, J. Comput. Anal. Appl. 21 (2016), 315–323.
[4] Y. Liang, H. Zeng and Z.-H. Zhou, Volterra-type operators from F(p,q,s) space to Bloch-Orlicz and Zygmund-Orlicz spaces, Filomat 34(4) (2020), 1359–1381. https://doi.org/10.2298/FIL2004359L
[5] B. D. MacCluer and and J. H. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), 878–906. https://doi.org/10.4153/CJM-1986-043-4
[6] A. Manavi, M. Hassanlou and H. Vaezi, Essential norm of generalized integral type operator from QK(p,q) to Zygmund spaces, Filomat 37(16) (2023), 5273–5282. https://doi.org/10.2298/FIL2316273M
[7] A. H. Sanatpour and M. Hassanlou, Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces, Filomat 31(9) (2017), 2877–2889. https://doi.org/10.2298/FIL1709877S
[8] J. H. Shapiro, The essential norm of a composition operator, Annals of Math. 127 (1987), 375–404. https://doi.org/10.2307/1971314
[9] S. Stević, Weighted differentiation composition operators from H∞ and Bloch spaces to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), 3634–3641. https://doi:10.1016/j.amc.2010.05.014
[10] W. Yang, Generalized weighted composition operators from the F(p,q,s) space to the Bloch-type space, Appl. Math. Comput. 218 (2012), 4967–4972. https://doi:10.1016/j.amc.2011.10.062
[11] X. Zhang, Ch. He and F. Cao, The equivalent norms of F(p,q,s) space in ℂn, J. Math. Anal. Appl. 401 (2013), 601–610. https://doi:10.1016/j.jmaa.2012.12.032
[12] R. Zhao, On a general family of function spaces, Ann. Acad. Sci. Fenn. Math. Dissertationes 105 (1996), 1–56.
[13] R. Zhao, On F(p,q,s) spaces, Acta Math. Scientia 41B(6) (2021), 1985–2020. https://doi.org/10.1007/s10473-021-0613-3
[14] K. Zhu, Bloch type spaces of analytic functions, Rocky Mt. J. Math. 23 (1993), 1143–1177. https://doi.org/10.1216/rmjm/1181072549
[15] X. Zhu, Weighted composition operators from F(p,q,s) spaces to Hμ∞ spaces, Abstr. Appl. Anal. 2009, Article ID 290978, 14 pages. https://doi.org/10.1155/2009/290978
Login:
