Title:
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Bloch type spaces on the unit ball of a Hilbert space (English) |
Author:
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Xu, Zhenghua |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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69 |
Issue:
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3 |
Year:
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2019 |
Pages:
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695-711 |
Summary lang:
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English |
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Category:
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math |
. |
Summary:
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We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented. (English) |
Keyword:
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Bloch type space |
Keyword:
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Lipschitz space |
Keyword:
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Hardy-Littlewood theorem |
Keyword:
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Hilbert space |
MSC:
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32A18 |
MSC:
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46E15 |
idZBL:
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Zbl 07088813 |
idMR:
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MR3989275 |
DOI:
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10.21136/CMJ.2018.0495-17 |
. |
Date available:
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2019-07-24T11:17:26Z |
Last updated:
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2021-10-04 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/147786 |
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Reference:
|
[1] Blasco, O., Galindo, P., Miralles, A.: Bloch functions on the unit ball of an infinite dimensional Hilbert space.J. Funct. Anal. 267 (2014), 1188-1204. Zbl 1293.32010, MR 3217061, 10.1016/j.jfa.2014.04.018 |
Reference:
|
[2] Chen, H.: Characterizations of $\alpha$-Bloch functions on the unit ball without use of derivative.Sci. China Ser. A 51 (2008), 1965-1981. Zbl 1187.32004, MR 2447421, 10.1007/s11425-008-0104-1 |
Reference:
|
[3] Chen, S., Ponnusamy, S., Rasila, A.: On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces.Math. Z. 279 (2015), 163-183. Zbl 1314.30116, MR 3299847, 10.1007/s00209-014-1361-z |
Reference:
|
[4] Dai, J., Wang, B.: Characterizations of some function spaces associated with Bloch type spaces on the unit ball of $\mathbb{C}^{n}$.J. Inequal. Appl. 2015 (2015), 10 pages. Zbl 1336.32006, MR 3411320, 10.1186/s13660-015-0846-6 |
Reference:
|
[5] Deng, F., Ouyang, C.: Bloch spaces on bounded symmetric domains in complex Banach spaces.Sci. China Ser. A 49 (2006), 1625-1632. Zbl 1114.32002, MR 2288219, 10.1007/s11425-006-2050-0 |
Reference:
|
[6] Graham, I., Kohr, G.: Geometric Function Theory in One and Higher Dimensions.Monographs and Textbooks in Pure and Applied Mathematics 255, Marcel Dekker, New York (2003). Zbl 1042.30001, MR 2017933, 10.1201/9780203911624 |
Reference:
|
[7] Hahn, K. T.: Holomorphic mappings of the hyperbolic space into the complex Euclidean space and the Bloch theorem.Canad. J. Math 27 (1975), 446-458. Zbl 0269.32014, MR 0466641, 10.4153/CJM-1975-053-0 |
Reference:
|
[8] Hardy, G. H., Littlewood, J. E.: Some properties of fractional integrals II.Math. Z. 34 (1932), 403-439. Zbl 0003.15601, MR 1545260, 10.1007/BF01180596 |
Reference:
|
[9] Holland, F., Walsh, D.: Criteria for membership of Bloch space and its subspace, BMOA.Math. Ann. 273 (1986), 317-335. Zbl 0561.30025, MR 0817885, 10.1007/BF01451410 |
Reference:
|
[10] Krantz, S. G.: Lipschitz spaces, smoothness of functions, and approximation theory.Exposition. Math. 1 (1983), 193-260. Zbl 0518.46018, MR 0782608 |
Reference:
|
[11] Krantz, S. G., Ma, D.: Bloch functions on strongly pseudoconvex domains.Indiana Univ. Math. J. 37 (1988), 145-163. Zbl 0628.32006, MR 0942099, 10.1512/iumj.1988.37.37007 |
Reference:
|
[12] Lehto, O., Virtanen, K. I.: Boundary behaviour and normal meromorphic functions.Acta Math. 97 (1957), 47-65. Zbl 0077.07702, MR 0087746, 10.1007/BF02392392 |
Reference:
|
[13] Li, S., Wulan, H.: Characterizations of $\alpha$-Bloch spaces on the unit ball.J. Math. Anal. Appl. 343 (2008), 58-63. Zbl 1204.32006, MR 2409457, 10.1016/j.jmaa.2008.01.023 |
Reference:
|
[14] Nowak, M.: Bloch space and Möbius invariant Besov spaces on the unit ball of $\mathbb{C}^{n}$.Complex Variables, Theory Appl. 44 (2001), 1-12. Zbl 1026.32011, MR 1826712, 10.1080/17476930108815339 |
Reference:
|
[15] Pavlović, M.: On the Holland-Walsh characterization of Bloch functions.Proc. Edinb. Math. Soc., II. Ser. 51 (2008), 439-441. Zbl 1165.30016, MR 2465917, 10.1017/S0013091506001076 |
Reference:
|
[16] Ren, G., Tu, C.: Bloch space in the unit ball of $\mathbb{C}^{n}$.Proc. Am. Math. Soc. 133 (2005), 719-726. Zbl 1056.32005, MR 2113920, 10.1090/S0002-9939-04-07617-8 |
Reference:
|
[17] Ren, G., Xu, Z.: Slice Lebesgue measure of quaternions.Adv. Appl. Clifford Algebr. 26 (2016), 399-416. Zbl 1337.30061, MR 3460007, 10.1007/s00006-015-0578-1 |
Reference:
|
[18] Rudin, W.: Function Theory in the Unit Ball of $\mathbb{C}^{n}$.Classics in Mathematics, Springer, Berlin (2008). Zbl 1139.32001, MR 2446682, 10.1007/978-3-540-68276-9 |
Reference:
|
[19] Timoney, R. M.: Bloch functions in several complex variables I.Bull. Lond. Math. Soc. 12 (1980), 241-267. Zbl 0416.32010, MR 0576974, 10.1112/blms/12.4.241 |
Reference:
|
[20] Timoney, R. M.: Bloch functions in several complex variables II.J. Reine Angew. Math. 319 (1980), 1-22. Zbl 0425.32008, MR 0586111, 10.1515/crll.1980.319.1 |
Reference:
|
[21] Yang, W., Ouyang, C.: Exact location of $\alpha$-Bloch spaces in $L^{p}_{a}$ and $H^{p}$ of a complex unit ball.Rocky Mountain J. Math. 30 (2000), 1151-1169. Zbl 0978.32002, MR 1797836, 10.1216/rmjm/1021477265 |
Reference:
|
[22] Zhang, M., Chen, H.: Equivalent characterizations of $\alpha$-Bloch functions on the unit ball.Acta Math., Sin. Engl. Ser. 27 (2011), 2395-2408. Zbl 1262.32002, MR 2853797, 10.1007/s10114-011-9391-5 |
Reference:
|
[23] Zhao, R.: A characterization of Bloch-type spaces on the unit ball of $\mathbb{C}^{n}$.J. Math. Anal. Appl. 330 (2007), 291-297. Zbl 1118.32006, MR 2302923, 10.1016/j.jmaa.2006.06.100 |
Reference:
|
[24] Zhu, K.: Bloch type spaces of analytic functions.Rocky Mt. J. Math. 23 (1993), 1143-1177. Zbl 0787.30019, MR 1245472, 10.1216/rmjm/1181072549 |
Reference:
|
[25] Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball.Graduate Texts in Mathematics 226, Springer, New York (2005). Zbl 1067.32005, MR 2115155, 10.1007/0-387-27539-8 |
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