Article
| Title: | Stević-Sharma type operators on Fock spaces in several variables (English) |
| Author: | Ma, Lijun |
| Author: | Yang, Zicong |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 1241-1263 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | Let $\varphi $ be an entire self-map of $\mathbb {C}^N$, $u_0$ be an entire function on $\mathbb {C}^N$ and ${\bf u}=(u_1,\cdots ,u_N)$ be a vector-valued entire function on $\mathbb {C}^N$. We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator $T_{u_0,{\bf u},\varphi }$ as follows: $$\openup -.4pt T_{u_0,{\bf u},\varphi }f=u_0\cdot f\circ \varphi +\sum _{i=1}^Nu_i\cdot \frac {\partial f}{\partial z_i}\circ \varphi . $$ We investigate the boundedness and compactness of $T_{u_0,{\bf u},\varphi }$ on Fock spaces. The complex symmetry and self-adjointness of $T_{u_0,{\bf u},\varphi }$ are also characterized. (English) |
| Keyword: | Stević-Sharma operator |
| Keyword: | Fock space |
| Keyword: | $\mathcal {J}$-symmetry |
| MSC: | 30H20 |
| MSC: | 46E15 |
| MSC: | 47B33 |
| DOI: | 10.21136/CMJ.2024.0244-24 |
| . | |
| Date available: | 2024-12-15T06:40:57Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152699 |
| . | |
| Reference: | [1] Arroussi, H., Tong, C.: Weighted composition operators between large Fock spaces in several complex variables.J. Funct. Anal. 277 (2019), 3436-3466. Zbl 1429.32011, MR 4001076, 10.1016/j.jfa.2019.04.008 |
| Reference: | [2] Carswell, B., MacCluer, B., Schuster, A.: Composition operators on the Fock space.Acta Sci. Math. 69 (2003), 871-887. Zbl 1051.47023, MR 2034214 |
| Reference: | [3] Chen, R.-Y., Yang, Z.-C., Zhou, Z.-H.: Unitary, self-adjointness and $\mathcal{J}$-symmetric weighted composition operators on Fock-Sobolev spaces.Oper. Matrices 16 (2022), 1139-1154. Zbl 1515.30124, MR 4543382, 10.7153/oam-2022-16-74 |
| Reference: | [4] Cowen, C. C., MacCluer, B. D.: Composition Operators on Spaces of Analytic Functions.Studies in Advanced Mathematics. CRC Press, Boca Raton (1995). Zbl 0873.47017, MR 1397026, 10.1201/9781315139920 |
| Reference: | [5] Garcia, S. R., Putinar, M.: Complex symmetric operators and applications.Trans. Am. Math. Soc. 358 (2006), 1285-1315. Zbl 1087.30031, MR 2187654, 10.1090/S0002-9947-05-03742-6 |
| Reference: | [6] Hai, P. V., Khoi, L. H.: Complex symmetry of weighted composition operators on the Fock space.J. Math. Anal. Appl. 433 (2016), 1757-1771. Zbl 1325.47057, MR 3398790, 10.1016/j.jmaa.2015.08.069 |
| Reference: | [7] Hai, P. V., Khoi, L. H.: Complex symmetric weighted composition operators on the Fock space in several variables.Complex Var. Elliptic Equ. 63 (2018), 391-405. Zbl 1390.32001, MR 3764769, 10.1080/17476933.2017.1315108 |
| Reference: | [8] Han, K., Wang, M.: Weighted composition operators on the Fock space.Sci. China, Math. 65 (2022), 111-126. Zbl 07462121, MR 4361970, 10.1007/s11425-020-1752-0 |
| Reference: | [9] Horn, R. A., Johnson, C. R.: Matrix Analysis.Cambridge University Press, Cambridge (2013). Zbl 1267.15001, MR 2978290, 10.1017/CBO9780511810817 |
| Reference: | [10] Hu, J., Li, S., Ou, D.: Embedding derivatives of Fock spaces and generalized weighted composition operators.J. Nonlinear Var. Anal. 5 (2021), 589-613. Zbl 1519.47041 |
| Reference: | [11] Hu, X., Yang, Z., Zhou, Z.: Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball.Int. J. Math. 31 (2020), Article ID 2050006, 21 pages. Zbl 1513.47048, MR 4060570, 10.1142/S0129167X20500068 |
| Reference: | [12] Hu, Z.: Equivalent norms on Fock spaces with some application to extended Cesàro operators.Proc. Am. Math. Soc. 141 (2013), 2829-2840. Zbl 1272.32003, MR 3056573, 10.1090/S0002-9939-2013-11550-9 |
| Reference: | [13] Hu, Z., Lv, X.: Toeplitz operators from one Fock space to another.Integral Equations Oper. Theory 70 (2011), 541-559. Zbl 1262.47044, MR 2819157, 10.1007/s00020-011-1887-y |
| Reference: | [14] Janson, S., Peetre, J., Rochberg, R.: Hankel forms and the Fock space.Rev. Math. Iberoam. 3 (1987), 61-138. Zbl 0704.47022, MR 1008445, 10.4171/RMI/46 |
| Reference: | [15] Le, T.: Normal and isometric weighted composition operators on Fock space.Bull. Lond. Math. Soc. 46 (2014), 847-856. Zbl 1298.47049, MR 3239622, 10.1112/blms/bdu046 |
| Reference: | [16] Liu, Y., Yu, Y.: Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball.J. Math. Anal. Appl. 423 (2015), 76-93. Zbl 1304.47046, MR 3273168, 10.1016/j.jmaa.2014.09.069 |
| Reference: | [17] Malhotra, A., Gupta, A.: Complex symmetry of generalized weighted composition operators on Fock space.J. Math. Anal. Appl. 495 (2021), Article ID 124740, 12 pages. Zbl 1461.30126, MR 4182951, 10.1016/j.jmaa.2020.124740 |
| Reference: | [18] Shapiro, J. H.: Composition Operators and Classical Function Theory.Universitext: Tracts in Mathematics. Springer, New York (1993). Zbl 0791.30033, MR 1237406, 10.1007/978-1-4612-0887-7 |
| Reference: | [19] Sharma, A. K.: Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces.Turk. J. Math. 35 (2011), 275-291. Zbl 1236.47025, MR 2839722, 10.3906/mat-0806-24 |
| Reference: | [20] Stević, S.: Weighted composition operators between Fock-type spaces in $\Bbb{C}^N$.Appl. Math. Comput. 215 (2009), 2750-2760. Zbl 1186.32003, MR 2563487, 10.1016/j.amc.2009.09.016 |
| Reference: | [21] Stević, S.: Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces.Appl. Math. Comput. 211 (2009), 222-233. Zbl 1165.30029, MR 2517681, 10.1016/j.amc.2009.01.061 |
| Reference: | [22] Stević, S.: Weighted iterated radial composition operators between some spaces of holomorphic functions on the unit ball.Abstr. Appl. Anal. 2010 (2020), Article ID 801264, 14 pages. Zbl 1207.47022, MR 2739686, 10.1155/2010/801264 |
| Reference: | [23] Stević, S.: On a new product-type operator on the unit ball.J. Math. Inequal. 16 (2022), 1675-1692. Zbl 1521.47070, MR 4532711, 10.7153/jmi-2022-16-109 |
| Reference: | [24] Stević, S.: Norm of the general polynomial differentiation composition operator from the space of Cauchy transforms to the $m$th weighted-type space on the unit disk.Math. Methods Appl. Sci. 47 (2024), 3893-3902. Zbl 07861229, MR 4730471, 10.1002/mma.9681 |
| Reference: | [25] Stević, S., Huang, C.-S., Jiang, Z.-J.: Sum of some product-type operators from Hardy spaces to weighted-type spaces on the unit ball.Math. Methods Appl. Sci. 45 (2022), 11581-11600. Zbl 07812790, MR 4509893, 10.1002/mma.8467 |
| Reference: | [26] Stević, S., Sharma, A. K.: On a product-type operator between Hardy and $\alpha$-Bloch spaces of the upper half-plane.J. Inequal. Appl. 2018 (2018), Article ID 273, 18 pages. Zbl 1506.47057, MR 3863081, 10.1186/s13660-018-1867-8 |
| Reference: | [27] Stević, S., Sharma, A. K., Bhat, A.: Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces.Appl. Math. Comput. 218 (2011), 2386-2397. Zbl 1244.30080, MR 2838149, 10.1016/j.amc.2011.06.055 |
| Reference: | [28] Stević, S., Sharma, A. K., Bhat, A.: Products of multiplication composition and differentiation operators on weighted Bergman spaces.Appl. Math. Comput. 217 (2011), 8115-8125. Zbl 1218.30152, MR 2802222, 10.1016/j.amc.2011.03.014 |
| Reference: | [29] Stević, S., Sharma, A. K., Krisham, R.: Boundedness and compactness of a new product-type operator from a general space to Bloch-type spaces.J. Inequal. Appl. 2016 (2016), Article ID 219, 32 pages. Zbl 1353.47065, MR 3546586, 10.1186/s13660-016-1159-0 |
| Reference: | [30] Tien, P. T., Khoi, L. H.: Differences of weighted composition operators between the Fock spaces.Monatsh. Math. 188 (2019), 183-193. Zbl 1508.47051, MR 3895397, 10.1007/s00605-018-1179-6 |
| Reference: | [31] Tien, P. T., Khoi, L. H.: Weighted composition operators between different Fock spaces.Potential Anal. 50 (2019), 171-195. Zbl 1411.30040, MR 3905527, 10.1007/s11118-017-9678-y |
| Reference: | [32] Tien, P. T., Khoi, L. H.: Weighted composition operators between Fock spaces in several variables.Math. Nachr. 293 (2020), 1200-1220. Zbl 07261550, MR 4107990, 10.1002/mana.201800197 |
| Reference: | [33] Ueki, S.-I.: Hilbert-Schmidt weighted composition operator on the Fock space.Int. J. Math. Anal., Ruse 1 (2007), 769-774. Zbl 1160.47306, MR 2370212 |
| Reference: | [34] Ueki, S.-I.: Weighted composition operator on the Fock space.Proc. Am. Math. Soc. 135 (2007), 1405-1410. Zbl 1126.47026, MR 2276649, 10.1090/S0002-9939-06-08605-9 |
| Reference: | [35] Ueki, S.-I.: Weighted composition operators on some function spaces of entire functions.Bull. Belg. Math. Soc. - Simon Stevin 17 (2010), 343-353. Zbl 1191.47032, MR 2663477, 10.36045/bbms/1274896210 |
| Reference: | [36] Wallstén, R.: The $S^p$-criterion for Hankel forms on the Fock space, $0<p<1$.Math. Scand. 64 (1989), 123-132. Zbl 0722.47025, MR 1036432, 10.7146/math.scand.a-12251 |
| Reference: | [37] Wang, S., Wang, M., Guo, X.: Differences of Stević-Sharma operators.Banach J. Math. Anal. 14 (2020), 1019-1054. Zbl 1508.47088, MR 4123322, 10.1007/s43037-019-00051-z |
| Reference: | [38] Wang, S., Wang, M., Guo, X.: Products of composition, multiplication and radial derivative operators between Banach spaces of holomorphic functions on the unit ball.Complex Var. Elliptic Equ. 65 (2020), 2026-2055. Zbl 1523.47041, MR 4170195, 10.1080/17476933.2019.1687455 |
| Reference: | [39] Zhao, L.: Invertible weighted composition operators on Fock space on $\Bbb{C}^N$.J. Funct. Spaces 2015 (2015), Article ID 250358, 5 pages. Zbl 1321.47065, MR 3361112, 10.1155/2015/250358 |
| Reference: | [40] Zhu, K.: Analysis on Fock Spaces.Graduate Texts in Mathematics 263. Springer, New York (2012). Zbl 1262.30003, MR 2934601, 10.1007/978-1-4419-8801-0 |
| Reference: | [41] Zhu, X.: Generalized weighted composition operators on weighted Bergman spaces.Numer. Funct. Anal. Optim. 30 (2009), 881-893. Zbl 1183.47030, MR 2555666, 10.1080/01630560903123163 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
