全纯函数空间上几个量的等价刻画问题

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1291-1299.

全纯函数空间上几个量的等价刻画问题

唐鹏程,张学军*(),吕睿昕

湖南师范大学数学与统计学院长沙 410006

收稿日期:2018-05-15 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 张学军 E-mail:xuejunttt@263.net
基金资助:
国家自然科学基金(11571104);湖南省研究生科研创新项目(CX2018B286)

Equivalent Characterization of Several Quantities on Holomorphic Function Spaces

Pengcheng Tang,Xuejun Zhang*(),Ruixin Lv

College of Mathematics and Statistics, Hunan Normal University, Changsha 410006

Received:2018-05-15 Online:2019-12-26 Published:2019-12-28
Contact: Xuejun Zhang E-mail:xuejunttt@263.net
Supported by:
the NSFC(11571104);the Hunan Provincial Innovation Foundation for Postgraduate(CX2018B286)

摘要/Abstract

摘要：

该文改进了多复变量单位球上一个常用函数在分式型微分和分式型积分作用后的表达式.同时该文改进了两个全纯函数空间上分式型微分的等价范数，去掉了等价范数中分式型微分R^s，t和R^β，t的约束条件β=s+N，其中N为某正整数.

关键词: 分式型导数, 分式型积分, 等价刻画, 单位球

Abstract:

In this paper, the expression under the action of fractional derivative and fractional integral for a common function on the unit ball of several complex variables is improved. At the same time, the equivalent norms of the fractional differential on two holomorphic function spaces are improved, and the constraint conditions β=s+N for the fractional differential R^{s, t} and R^{β, t} in the equivalent norms are removed, where N is a positive integer.

Key words: Fractional derivative, Fractional integral, Equivalent characterization, Unit ball

中图分类号:

O174.56

唐鹏程,张学军,吕睿昕. 全纯函数空间上几个量的等价刻画问题[J]. 数学物理学报, 2019, 39(6): 1291-1299.

Pengcheng Tang,Xuejun Zhang,Ruixin Lv. Equivalent Characterization of Several Quantities on Holomorphic Function Spaces[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1291-1299.

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