| Title:
|
Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space (English) |
| Author:
|
Li, Songxiao |
| Author:
|
Qian, Ruishen |
| Author:
|
Zhou, Jizhen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
629-643 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space. (English) |
| Keyword:
|
Bloch space |
| Keyword:
|
weighted Bergman space |
| Keyword:
|
Hardy space |
| Keyword:
|
essential norm |
| Keyword:
|
weighted composition operator |
| MSC:
|
30H30 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 06770121 |
| idMR:
|
MR3697907 |
| DOI:
|
10.21136/CMJ.2017.0481-15 |
| . |
| Date available:
|
2017-09-01T12:20:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146850 |
| . |
| Reference:
|
[1] Castillo, R. E., Ramos-Fernández, J. C., Rojas, E. M.: A new essential norm estimate of composition operators from weighted Bloch space into $\mu$-Bloch spaces.J. Funct. Spaces Appl. 2013 (2013), Article ID 817278, 5 pages. Zbl 06281096, MR 3111830, 10.1155/2013/817278 |
| Reference:
|
[2] Colonna, F.: New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space.Cent. Eur. J. Math. 11 (2013), 55-73. Zbl 1279.47041, MR 2988782, 10.2478/s11533-012-0097-4 |
| Reference:
|
[3] 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 |
| Reference:
|
[4] Esmaeili, K., Lindström, M.: Weighted composition operators between Zygmund type spaces and their essential norms.Integral Equations Oper. Theory 75 (2013), 473-490. Zbl 1306.47036, MR 3032664, 10.1007/s00020-013-2038-4 |
| Reference:
|
[5] Hyvärinen, O., Kemppainen, M., Lindström, M., Rautio, A., Saukko, E.: The essential norm of weighted composition operators on weighted Banach spaces of analytic functions.Integral Equations Oper. Theory 72 (2012), 151-157. Zbl 1252.47026, MR 2872471, 10.1007/s00020-011-1919-7 |
| Reference:
|
[6] Hyvärinen, O., Lindström, M.: Estimates of essential norms of weighted composition operators between Bloch-type spaces.J. Math. Anal. Appl. 393 (2012), 38-44. Zbl 1267.47040, MR 2921646, 10.1016/j.jmaa.2012.03.059 |
| Reference:
|
[7] Li, S., Stević, S.: Weighted composition operators from Bergman-type spaces into Bloch spaces.Proc. Indian Acad. Sci., Math. Sci. 117 (2007), 371-385. Zbl 1130.47016, MR 2352056, 10.1007/s12044-007-0032-y |
| Reference:
|
[8] Li, S., Stević, S.: Generalized composition operators on Zygmund spaces and Bloch type spaces.J. Math. Anal. Appl. 338 (2008), 1282-1295. Zbl 1135.47021, MR 2386496, 10.1016/j.jmaa.2007.06.013 |
| Reference:
|
[9] Li, S., Stević, S.: Weighted composition operators from Zygmund spaces into Bloch spaces.Appl. Math. Comput. 206 (2008), 825-831. Zbl 1215.47022, MR 2483058, 10.1016/j.amc.2008.10.006 |
| Reference:
|
[10] Liang, Y.-X., Zhou, Z.-H.: Essential norm of the product of differentiation and composition operators between Bloch-type spaces.Arch. Math. 100 (2013), 347-360. Zbl 1276.47041, MR 3044119, 10.1007/s00013-013-0499-y |
| Reference:
|
[11] Lou, Z.: Composition operators on Bloch type spaces.Analysis Münich 23 (2003), 81-95. Zbl 1058.47024, MR 1983976, 10.1524/anly.2003.23.1.81, |
| Reference:
|
[12] MacCluer, B. D., Zhao, R.: Essential norms of weighted composition operators between Bloch-type spaces.Rocky Mountain J. Math. 33 (2003), 1437-1458. Zbl 1061.30023, MR 2052498, 10.1216/rmjm/1181075473 |
| Reference:
|
[13] Madigan, K., Matheson, A.: Compact composition operators on the Bloch space.Trans. Am. Math. Soc. 347 (1995), 2679-2687. Zbl 0826.47023, MR 1273508, 10.1090/S0002-9947-1995-1273508-X |
| Reference:
|
[14] Manhas, J. S., Zhao, R.: New estimates of essential norms of weighted composition operators between Bloch type spaces.J. Math. Anal. Appl. 389 (2012), 32-47. Zbl 1267.47042, MR 2876478, 10.1016/j.jmaa.2011.11.039 |
| Reference:
|
[15] Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions.J. Lond. Math. Soc., II. Ser. 61 (2000), 872-884. Zbl 0959.47016, MR 1766111, 10.1112/S0024610700008875 |
| Reference:
|
[16] Ohno, S., Stroethoff, K., Zhao, R.: Weighted composition operators between Bloch-type spaces.Rocky Mt. J. Math. 33 (2003), 191-215. Zbl 1042.47018, MR 1994487, 10.1216/rmjm/1181069993 |
| Reference:
|
[17] Stević, S.: 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. Zbl 1195.30073, MR 2661728, 10.1016/j.amc.2010.05.014 |
| Reference:
|
[18] Stević, S.: Characterizations of composition followed by differentiation between Bloch-type spaces.Appl. Math. Comput. 218 (2011), 4312-4316. Zbl 1244.30082, MR 2862100, 10.1016/j.amc.2011.10.004 |
| Reference:
|
[19] Tjani, M.: Compact Composition Operators on Some Möbius Invariant Banach Spaces.PhD Thesis, Michigan State University, Michigan (1996). MR 2695395 |
| Reference:
|
[20] Tjani, M.: Compact composition operators on Besov spaces.Trans. Am. Math. Soc. 355 (2003), 4683-4698. Zbl 1045.47020, MR 1990767, 10.1090/S0002-9947-03-03354-3 |
| Reference:
|
[21] Wulan, H., Zheng, D., Zhu, K.: Compact composition operators on BMOA and the Bloch space.Proc. Am. Math. Soc. 137 (2009), 3861-3868. Zbl 1194.47038, MR 2529895, 10.1090/S0002-9939-09-09961-4 |
| Reference:
|
[22] Xiong, C.: Norm of composition operators on the Bloch space.Bull. Aust. Math. Soc. 70 (2004), 293-299. Zbl 1062.30038, MR 2094297, 10.1017/S0004972700034511 |
| Reference:
|
[23] Yang, W.: Generalized weighted composition operators from the $F(p,q,s)$ space to the Bloch-type space.Appl. Math. Comput. 218 (2012), 4967-4972. Zbl 1244.30083, MR 2870021, 10.1016/j.amc.2011.10.062 |
| Reference:
|
[24] Yang, W., Zhu, X.: Generalized weighted composition operators from area Nevanlinna spaces to Bloch-type spaces.Taiwanese J. Math. 16 (2012), 869-883. Zbl 1268.47034, MR 2917244, 10.11650/twjm/1500406662 |
| Reference:
|
[25] Zhao, R.: Essential norms of composition operators between Bloch type spaces.Proc. Am. Math. Soc. 138 (2010), 2537-2546. Zbl 1190.47028, MR 2607883, 10.1090/S0002-9939-10-10285-8 |
| Reference:
|
[26] Zhu, K.: Operator Theory in Function Spaces.Pure and Applied Mathematics 139, Marcel Dekker, New York (1990). Zbl 0706.47019, MR 1074007 |
| Reference:
|
[27] Zhu, X.: Generalized weighted composition operators on Bloch-type spaces.J. Inequal. Appl. (electronic only) 2015 (2015), Paper No. 59, 9 pages. Zbl 1309.47027, MR 3313862, 10.1186/s13660-015-0580-0 |
| . |
