This paper investigates the boundedness and compactness of generalized weighted composition operators on the closure of analytic tent spaces within the Korenblum space. It further analyzes the boundedness, compactness, and essential norm of these operators when acting from the Korenblum space to analytic tent spaces.
Citation: Xiangling Zhu, Rong Yang, Songxiao Li. Generalized weighted composition operators mapping into analytic tent spaces and its closure in the Korenblum space[J]. AIMS Mathematics, 2025, 10(9): 21452-21467. doi: 10.3934/math.2025953
This paper investigates the boundedness and compactness of generalized weighted composition operators on the closure of analytic tent spaces within the Korenblum space. It further analyzes the boundedness, compactness, and essential norm of these operators when acting from the Korenblum space to analytic tent spaces.
| [1] | J. Anderson, J. Clunie, C. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math., 270 (1974), 12–37. https://doi.org/10.1515/crll.1974.270.12 |
| [2] | R. Aulaskari, R. Zhao, Composition operators and closures of some Möbius invariant spaces in the Bloch space, Math. Scand., 107 (2010), 139–149. https://doi.org/10.7146/math.scand.a-15147 |
| [3] |
J. Chen, Closures of holomorphic tent spaces in weighted Bloch spaces, Complex Anal. Oper. Theory, 17 (2023), 87. https://doi.org/10.1007/s11785-023-01389-x doi: 10.1007/s11785-023-01389-x
|
| [4] |
P. Coifman, Y. Meyer, E. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal., 62 (1985), 304–335. https://doi.org/10.1016/0022-1236(85)90007-2 doi: 10.1016/0022-1236(85)90007-2
|
| [5] | C. Cowen, B. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995. |
| [6] |
P. Ghatage, D. Zheng, Analytic functions of bounded mean oscillation and the Bloch space, Integr. Equat. Oper. Th., 17 (1993), 501–515. https://doi.org/10.1007/BF01200391 doi: 10.1007/BF01200391
|
| [7] |
E. Gómez-Orts, Weighted composition operators on Korenblum type spaces of analytic functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 114 (2020), 199. https://doi.org/10.1007/s13398-020-00924-1 doi: 10.1007/s13398-020-00924-1
|
| [8] |
W. He, L. Jiang, Composition operator on Bers-type spaces, Acta Math. Sci. (Engl. Ed.), 22 (2002), 404–412. https://doi.org/10.1016/S0252-9602(17)30310-7 doi: 10.1016/S0252-9602(17)30310-7
|
| [9] | F. Pérez-Gonzáleza, J. Rättyä, Forelli–Rudin estimates, Carleson measures and $F(p, q, s)$-functions, J. Math. Anal. Appl., 315 (2006), 394–414. https://doi.org/10.1016/j.jmaa.2005.10.034 |
| [10] | R. Qian, S. Li, Composition operators and closures of Dirichlet type spaces $\mathcal{D}_\alpha$ in the logarithmic Bloch space, Indag. Math. (N.S.), 29 (2018), 1432–1440. |
| [11] |
S. Stević, Weighted differntiation composition operators from mixed-norm spaces to weighted-type spaces, Appl. Math. Comput., 211 (2009), 222–233. https://doi.org/10.1016/j.amc.2009.01.061 doi: 10.1016/j.amc.2009.01.061
|
| [12] |
S. Stević, Weighted differentiation composition operators from the mixed-norm space to the $n$th weigthed-type space on the unit disk, Abstr. Appl. Anal., 2010 (2010), 246287. https://doi.org/10.1155/2010/246287 doi: 10.1155/2010/246287
|
| [13] |
S. Stević, Weighted differentiation composition operators from $H^\infty$ and Bloch spaces to $n$th weighted-type spaces on the unit disk, Appl. Math. Comput., 216 (2010), 3634–3641. https://doi.org/10.1016/j.amc.2010.05.014 doi: 10.1016/j.amc.2010.05.014
|
| [14] | S. Ueki, Weighted composition operators acting between the $N_p$-space and the weighted-type space $H^{\infty}_{\alpha}$, Indag. Math. (N.S.), 23 (2012), 243–255. |
| [15] | M. Wang, Y. Liu, Weighted composition operators between Bers-type spaces, Acta Math. Sci. (Chinese Ed.), 27 (2007), 665–671. |
| [16] |
C. Yang, W. Xu, Spaces with normal weights and Hadamard gap series, Arch. Math. (Basel), 96 (2011), 151–160. https://doi.org/10.1007/s00013-011-0223-8 doi: 10.1007/s00013-011-0223-8
|
| [17] |
K. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math., 23 (1993), 1143–1177. https://doi.org/10.1216/rmjm/1181072549 doi: 10.1216/rmjm/1181072549
|
| [18] |
X. Zhu, Products of differentiation, composition and multiplication from Bergman type spaces to Bers type space, Integr. Transf. Spec. F., 18 (2007), 223–231. https://doi.org/10.1080/10652460701210250 doi: 10.1080/10652460701210250
|
| [19] |
X. Zhu, Generalized weighted composition operators on weighted Bergman spaces, Numer. Funct. Anal. Opt., 30 (2009), 881–893. https://doi.org/10.1080/01630560903123163 doi: 10.1080/01630560903123163
|
| [20] |
X. Zhu, Generalized weighted composition operators from Bloch spaces into Bers-type spaces, Filomat, 26 (2012), 1163–1169. https://doi.org/10.2298/FIL1206163Z doi: 10.2298/FIL1206163Z
|
| [21] |
X. Zhu, Essential norm of generalized weighted composition operators on Bloch-type spaces, Appl. Math. Comput., 274 (2016), 133–142. https://doi.org/10.1016/j.amc.2015.10.061 doi: 10.1016/j.amc.2015.10.061
|
| [22] |
X. Zhu, Q. Hu, D. Qu, Polynomial differentiation composition operators from Besov-type spaces into Bloch-type spaces, Math. Methods Appl. Sci., 47 (2024), 147–168. https://doi.org/10.1002/mma.9647 doi: 10.1002/mma.9647
|
| [23] | A. Zygmund, Trigonometric Series, Cambridge Univ. Press, London, 1959. |
Xiangling Zhu, Rong Yang, Songxiao Li. Generalized weighted composition operators mapping into analytic tent spaces and its closure in the Korenblum space[J]. AIMS Mathematics, 2025, 10(9): 21452-21467. doi: 10.3934/math.2025953
DownLoad: