多重调和函数空间的对偶空间

何莉, 曹广福

数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 833-840.

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数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 833-840. DOI: 10.12386/A2015sxxb0082
论文

多重调和函数空间的对偶空间

    何莉, 曹广福
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The Dual Space of Pluriharmonic Function Space

    Li HE, Guang Fu CAO
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摘要

研究了多重调和函数空间及其上的复合算子, 给出了多重调和函数空间的对偶空间, 刻画了该类空间上复合算子的有界性, 紧性和Fredholm性.

Abstract

We consider the pluriharmonic function space and the composition operators on it, mainly about characterizing the dual space of pluriharmonic function space, describing the boundedness, compactness and Fredholmness of composition operators.

关键词

多重调和函数 / 对偶空间 / 复合算子

Key words

pluriharmonic function / dual space / composition operator

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何莉, 曹广福. 多重调和函数空间的对偶空间. 数学学报, 2015, 58(5): 833-840 https://doi.org/10.12386/A2015sxxb0082
Li HE, Guang Fu CAO. The Dual Space of Pluriharmonic Function Space. Acta Mathematica Sinica, Chinese Series, 2015, 58(5): 833-840 https://doi.org/10.12386/A2015sxxb0082

参考文献

[1] Cao G. F., Elias N., Ghatage P., et al., Composition operators on a Banach space of analytic functions, Acta Math. Sinica, New Ser., 1998, 14(2): 201-208.

[2] Cao G. F., Sun S. H., On composition operators on Hp-spaces in several variables, Acta Mathmatica Sinica, 1997, 13(2): 281-288.

[3] Cowen C. C., MacCluer B. D., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.

[4] Figura D. B., Composition operators on Hardy space in several complex variables, J. Math. Anal. Appl., 1985, 109(2): 340-354.

[5] MacCluer B. D., Compact composition operators on Hp(BN), Michigan Math. J., 1985, 32(2): 237-248.

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

[7] Xu X. M., Theory of Composion Operator, Science Press, Beijing, 1999.

[8] Zhu K. H., Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.

基金

国家自然科学基金资助项目(11271092);广东省教育部博士点专项基金资助项目(20114410110001)

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