Generalized weighted composition operators from minimal Möbius invariant spaces into $n$th weighted ‎spaces

Document Type : Original Paper

Authors

1 Department of Mathematics,, Mahabad Branch,, Islamic Azad University,, Mahabad,, Iran

2 Department of Mathematics‎, ‎Urima Branch‎, ‎Islamic Azad University‎, ‎Urima‎, ‎Iran

3 Department of mathematics, Faculty of mathematics and statistics, university of Isfahan, Isfahan Iran.

Abstract

‎In this paper‎, ‎we first study the boundedness of generalized‎ weighted composition operators from minimal Möbius invariant‎ ‎subspace to the $n$th weighted type space‎. ‎Then‎, ‎we obtain‎ ‎equivalence conditions for its boundedness by using the Bell‎ ‎polynomials‎. ‎We also find some estimates for the essential‎ ‎norm of this operator and use them to present equivalence‎ ‎conditions for the compactness of such an operator‎.

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References

[۱ [عباسی، ابراهیم، نصراصفهانی، سپیده و خلیل پور، کمال. ۱۴۰۰ .عملگر استویچ شارما از فضای بسوف به فضای
زیگموند. مجله مدلسازی پیشرفته ریاضی، ۳)۱۱ ،(صص. ۵۷۳ −۵۸۴.
ⅮOI: ۱۹۳۰ .۳۷۳۶۹ .۲۰۲۱ .JAⅯⅯ/۲۲۰۵۵ .۱۰
[2] Abbasi, E. Vaezi, H. and Li, S., 2019. Essential norm of weighted composition operators from H∞to nth weighted type spaces. Mediterr. J. Math., 16, pp. 133. doi.org/10.1007/s00009­019­1409­8
[3] Abbasi, E. and Vaezi, H., 2020. Estimates of essential norm of generalized weighted composition operators from Bloch type spaces to nth weighted type spaces. Math. Slovaca, 70(1), pp. 71­80. doi.org/10.1515/ms­2017­0332
[4] Arazy, J. Fisher, S. and Peetre, J., 1986. Möbius invariant function spaces. J. Reine angew. Math.,
363, pp. 110­145. doi.org/10.1515/crll.1985.363.110
[5] Comter, L., 1974. Advanced Combinatiories. D. Reidel, Dordrecht.
[6] Hassanlou, M. Abbasi, E. Kanani Arpatapeh, M. and Nasresfahani, S., 2023. Product type operators between Minimal Möbius invariant spaces and Zygmund type spaces. Sahand Commun. Math. Anal.,20(3), pp. 69­80. doi.org/10.22130/scma.2023.560164.1163
[7] Rubel, L., 1979. An extremal property of the Bloch space. Proc. Am. Math. Soc., 75(1), pp. 45­49.
doi.org/10.2307/2042668
[8] Stevic, S., 2010. Weighted differentiation composition operators from H∞ and Bloch spaces to
nth weighted­type spaces on the unit disk. J. Appl. Math. Comput., 216 (12), pp. 3634­3641.
doi.org/10.1016/j.amc.2010.05.014
[9] Tjani, M., 2003. Compact composition operators on Besov spaces. Trans. Amer. Math Soc., 355, pp. 4683­4698. S 0002­9947­(03)03354­3
[10] Tjani, M., 1996. Compact composition operators on some Möbius invariant Banach space. Ph. D.thesis, Michigan State university, Michigan.
[11] Zhu, K., 2007. Operator Theory in Function Spaces. second ed., Mathematical surveys and Monographs, 138, Amer. Math. Soc., Providence, RI.
[12] Zhu, K., 1993. Bloch type space of analytic functions. Rocky Mountain J. Math., 23(3), pp. 1143­1177. doi: 1216/rmjm/1181072549
[13] Zhu, X., 2007. Products of differentiation, composition and multiplication from Bergman
type spaces to Bers type spaces. Integ. Trans. Spec. Funct., 18(3), pp. 223­231.
doi.org/10.1080/10652460701210250
[14] Zhu, X. Abbasi, E. and Ebrahimi, A., 2021. A class of operator­related composition operators from the Besov spaces into the Bloch space. Bulletin of the iranian mathematical society, 47, 171–184. doi.org/10.1007/s41980­020­00374­w
[15] Zhu, X., (2020). Weighted composition operators from the minimal Möbius invariant space into nth weighted­type spaces, Ann. Func. Anal., 2, 379–390. doi.org/10.1007/s43034­019­00010­7

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History

  • Receive Date: 07 January 2024
  • Revise Date: 08 June 2024
  • Accept Date: 08 September 2024

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