Abstract
A family of Zygmund-type spaces, called Dirichlet–Zygmund-type spaces, are introduced. The boundedness, compactness and the essential norm of weighted composition operators from Dirichlet–Zygmund-type spaces into Stević-type spaces are also investigated in this paper.
Funding statement: The author is supported by the Foundation for Scientific and Technological Innovation in Higher Education of Guangdong (no. 2021KTSCX182), GuangDong Basic and Applied Basic Research Foundation (no. 2022A1515010317).
References
[1] E. Abbasi and S. Li, Weighted composition operators from the Zygmund space to nth weighted-type spaces, Numer. Funct. Anal. Optim. 41 (2020), no. 12, 1472–1494. 10.1080/01630563.2020.1777158Search in Google Scholar
[2] E. Abbasi, S. Li and H. Vaezi, Weighted composition operators from the Bloch space to nth weighted-type spaces, Turkish J. Math. 44 (2020), no. 1, 108–117. 10.3906/mat-1907-34Search in Google Scholar
[3]
E. Abbasi, H. Vaezi and S. Li,
Essential norm of weighted composition operators from
[4] S. Alyusof and F. Colonna, Operator norms and essential norms of weighted composition operators from analytic function spaces into Zygmund-type spaces, Complex Anal. Oper. Theory 14 (2020), no. 6, Paper No. 62. 10.1007/s11785-020-01018-xSearch in Google Scholar
[5] J. Arazy, S. D. Fisher and J. Peetre, Möbius invariant function spaces, J. Reine Angew. Math. 363 (1985), 110–145. 10.1515/crll.1985.363.110Search in Google Scholar
[6] F. Colonna and S. Li, Weighted composition operators from the minimal Möbius invariant space into the Bloch space, Mediterr. J. Math. 10 (2013), no. 1, 395–409. 10.1007/s00009-012-0182-8Search in Google Scholar
[7]
F. Colonna and M. Tjani,
Weighted composition operators from the Besov spaces into the weighted-type space
[8] F. Colonna and M. Tjani, Operator norms and essential norms of weighted composition operators between Banach spaces of analytic functions, J. Math. Anal. Appl. 434 (2016), no. 1, 93–124. 10.1016/j.jmaa.2015.08.073Search in Google Scholar
[9] C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Stud. Adv. Math., CRC Press, Boca Raton, 1995. Search in Google Scholar
[10] J. Du, S. Li and Y. Zhang, Essential norm of weighted composition operators on Zygmund-type spaces with normal weight, Math. Inequal. Appl. 21 (2018), no. 3, 701–714. 10.7153/mia-2018-21-49Search in Google Scholar
[11] Q. Hu and X. Zhu, Essential norm of weighted composition operators from the Lipschtiz space to the Zygmund space, Bull. Malays. Math. Sci. Soc. 41 (2018), no. 3, 1293–1307. 10.1007/s40840-016-0391-6Search in Google Scholar
[12] S. Li and S. Stević, Volterra-type operators on Zygmund spaces, J. Inequal. Appl. 2007 (2007), Article ID 32124. 10.1155/2007/32124Search in Google Scholar
[13] S. Li and S. Stević, Generalized weighted composition operators from α-Bloch spaces into weighted-type spaces, J. Inequal. Appl. 2015 (2015), Article ID 265. 10.1186/s13660-015-0770-9Search in Google Scholar
[14] A. Montes-Rodríguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. Lond. Math. Soc. (2) 61 (2000), no. 3, 872–884. 10.1112/S0024610700008875Search in Google Scholar
[15] B. Sehba and S. Stević, On some product-type operators from Hardy–Orlicz and Bergman–Orlicz spaces to weighted-type spaces, Appl. Math. Comput. 233 (2014), 565–581. 10.1016/j.amc.2014.01.002Search in Google Scholar
[16] S. Stević, Composition operators from the weighted Bergman space to the nth weighted spaces on the unit disc, Discrete Dyn. Nat. Soc. 2009 (2009), Article ID 742019. 10.1155/2009/742019Search in Google Scholar
[17] S. Stević, On an integral operator from the Zygmund space to the Bloch-type space on the unit ball, Glasg. Math. J. 51 (2009), no. 2, 275–287. 10.1017/S0017089508004692Search in Google Scholar
[18]
S. Stević,
Composition followed by differentiation from
[19] S. Stević, On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball, Abstr. Appl. Anal. 2010 (2010), Article ID 198608. 10.1155/2010/198608Search in Google Scholar
[20]
S. Stević,
Weighted differentiation composition operators from
[21] S. Stević, Weighted differentiation composition operators from the mixed-norm space to the nth weighted-type space on the unit disk, Abstr. Appl. Anal. 2010 (2010), Article ID 246287. 10.1155/2010/246287Search in Google Scholar
[22] S. Stević, Essential norm of some extensions of the generalized composition operators between kth weighted-type spaces, J. Inequal. Appl. 2017 (2017), Paper No. 220. 10.1186/s13660-017-1493-xSearch in Google Scholar PubMed PubMed Central
[23] S. Stević, A. K. Sharma and A. Bhat, Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 218 (2011), no. 6, 2386–2397. 10.1016/j.amc.2011.06.055Search in Google Scholar
[24] K. Zhu, Operator Theory in Function Spaces, 2nd ed., Math. Surveys Monogr. 138, American Mathematical Society, Providence, 2007. 10.1090/surv/138Search in Google Scholar
[25] X. Zhu, Weighted composition operators from Dirichlet-type spaces into Stević-type spaces, Math. Inequal. Appl. 23 (2020), no. 4, 1311–1323. 10.7153/mia-2020-23-97Search in Google Scholar
[26] X. Zhu, Weighted composition operators from the minimal Möbius invariant space into n-th weighted-type spaces, Ann. Funct. Anal. 11 (2020), no. 2, 379–390. 10.1007/s43034-019-00010-7Search in Google Scholar
[27] X. Zhu and J. Du, Weighted composition operators from weighted Bergman spaces to Stević-type spaces, Math. Inequal. Appl. 22 (2019), no. 1, 361–376. 10.7153/mia-2019-22-27Search in Google Scholar
[28] X. Zhu and N. Hu, Weighted composition operators from Besov Zygmund-type spaces into Zygmund-type spaces, J. Funct. Spaces 2020 (2020), Article ID 2384971. 10.1155/2020/2384971Search in Google Scholar
[29] Wikipedia, https://en.wikipedia.org/wiki/Bell_polynomials. Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston