CnF(p,q,s)空间的等价刻画及应用

张学军, 肖建斌, 胡朝辉, 刘亚玲, 熊东红, 吴燕

数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 1029-1042.

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数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 1029-1042. DOI: 10.12386/A2011sxxb0102
论文

CnF(p,q,s)空间的等价刻画及应用

    张学军1, 肖建斌2, 胡朝辉1, 刘亚玲1, 熊东红1, 吴燕1
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Equivalent Characterization and Application of F(p,q,s) Space in Cn

    Xue Jun ZHANG1, Jian Bin XIAO2, Zhao Hui HU1, Yaling LIU1, Dong Hong XIONG1, Yan WU1
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摘要

设 0 < p < ∞, 0 ≤ s < ∞, max{-n-1,-s-1} < q < ∞,本文探讨了Cn 中单位球BF(p,q,s)空间的等价刻画问题,给出了F(p,q,s)空间的高阶导数刻画方式.同时,作为应用,还讨论了F(p,q,s)空间上的点乘子.  

Abstract

Let 0 < p < ∞, 0 ≤ s < ∞, max{-n-1,-s-1} < q < ∞. In this paper, we will discuss the equivalent characterization of F(p,q,s) space on the unit ball B in Cn, and give the characterization of high order derivative to F(p,q,s) space. At the same time, as a application, we will discuss the point-wise multiplier of F(p,q,s) space.  

关键词

F(p / q / s)空间 / 等价刻画 / 点乘子

Key words

F(p,q,s) space / equivalent characterization / point-wise multiplier

引用本文

导出引用
张学军, 肖建斌, 胡朝辉, 刘亚玲, 熊东红, 吴燕. CnF(p,q,s)空间的等价刻画及应用. 数学学报, 2011, 54(6): 1029-1042 https://doi.org/10.12386/A2011sxxb0102
Xue Jun ZHANG, Jian Bin XIAO, Zhao Hui HU, Yaling LIU, Dong Hong XIONG, Yan WU. Equivalent Characterization and Application of F(p,q,s) Space in Cn. Acta Mathematica Sinica, Chinese Series, 2011, 54(6): 1029-1042 https://doi.org/10.12386/A2011sxxb0102

参考文献

[1] Jiang L. J., He Y. Z., Composition operators from βα to F(p,q,s), Acta Math. Scientia, 2003, 23B(2): 252-260.

[2] Zhou Z. H., Chen R. Y., Weighted composition operator from F(p,q,s) to Bloch type spaces on the unit ball, Int. J. Math., 2008, 19(8): 899-926.

[3] Zhang X. J., Xiao J. B., Weighted composition operator between two analytic function spaces, Adv. Math., 2006, 35(4): 453-462 (in Chinese).

[4] Zhang X. J., Xiao J. B., Weighted composition operators between μ-Bloch spaces on the unit ball, Science in China, 2005, 48A(10): 1349-1368.

[5] Zhuo W. X., Ouyang C. H., Möbius invariant gradient and little α-Bloch functions, Acta Math. Scientia, 2002, 22B(3): 295-301.

[6] Zhu K. H., Spaces of Holomorphic Functions in the Unit Ball, New York: Springer-Verlag (GTM 226), 2005.

[7] Ortega J., Fabrega J., Pointwise multipliers and Corona type decomposition in BMOA, Ann. Inst. Fourier, 1996, 46: 111-137 (Grenoble).

[8] Rudin W., Function Theory in the Unit Ball of Cn, New York: Springer-Verlag, 1980.

[9] Hu Z. J., Extended Ces`aro operators on mixed norm spaces, Proc. Amer.Math. Soc., 2003, 131: 2171-2179.

[10] Shi J. H., Ren G. B., Boundedness of the Ces`aro operator on mixed norm spaces, Proc. Amer. Math. Soc., 1998, 126: 3553-3560.

[11] Lou Z. J., Composition operators on Bloch type spaces, Analysis, 2003, 23(1): 81-95.

[12] Wulan H. S., Compactness of the composition operators from the Bloch space B to Qk spaces, Acta Math. Sinica, English Series, 2005, 21(6): 1415-1424.

[13] Ouyang C. H., Yang W. S., Zhao R. H., Characterizations of Bergman spaces and Bloch space in the unit ball of Cn, Trans. Amer. Math. Soc., 1995, 347: 4301-4319.

[14] Chen H. H., Bounded-ness below of composition operator on Bloch space, Science in China, 2003, 33A(4): 289-296 (in Chinese).

[15] Shi J. H., Luo L., Composition operators on the Bloch space of several complex variables, Acta Mathematica Sinica, English Series, 2000, 16(1): 85-98.

[16] Zhang X. J., Xiao J. B., Hu Z. J., The multipliers between the mixed norm space in Cn, J. Math. Anal. Appl., 2005, 311(2): 664-674.

[17] Hu P. Y., Shi J. H., Multipliers on Dirichlet type spaces, Acta Math. Sinica, 2001, 17(2): 263-272.

[18] Zhang X. J., Wang M., The pointwise multipliers of p-Bloch space in the unit ball of Cn, J. of Math. Study, 34(2): 158-16 (in Chinese).

[19] Axler S., Shields A. L., Univalent multipliers of the Dieichlet space, Michigan Math. J., 1985, 32: 65-80.

[20] Zhu K. H., Multipliers of BMO in the Bergman metric with applications to Toeplitz operators, J. Funct. Anal., 1989, 87: 31-50.

[21] Stegenga D. A., Multipliers of the Dirichlet space, Illinois J. Math., 1980, 24: 113-139.

[22] Zhang X. J., The pointwise multipliers of Bloch type space βp and Dirichlet type space Dq on the unit ball of Cn, J. Math. Anal. Appl., 2003, 385(2): 376-386.

[23] Taylor G. D., Multipliers on Dα, Trans. Amer. Math. Soc., 1966, 123: 229-240.

[24] Zhang X. J., The multipliers on several holomorphic function spaces, Chin. J. Conte. Math., 2005, 26(3): 249-258.

基金

湖南省教育厅重点基金项目(10A074)

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