[1]戴绍虞,潘一飞.关于微分算子Δ2+a的一个注记[J].南京师范大学学报(自然科学版),2020,43(03):7-11.[doi:10.3969/j.issn.1001-4616.2020.03.002]
　Dai Shaoyu,Pan Yifei.A Note on the Differential Operator Δ2+a[J].Journal of Nanjing Normal University(Natural Science Edition),2020,43(03):7-11.[doi:10.3969/j.issn.1001-4616.2020.03.002]
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年03期
页码:
7-11
栏目:
·数学·
出版日期:
2020-09-30

文章信息/Info

Title:
A Note on the Differential Operator Δ2+a
文章编号:
1001-4616(2020)03-0007-05
作者:
戴绍虞1; 潘一飞2
(1.金陵科技学院理学院,江苏 南京 211169)(2.美国普渡大学韦恩堡校区数学系,印第安纳州 韦恩堡 46805)
Author(s):
Dai Shaoyu1; Pan Yifei2
(1.Jingling Institute of Technology,Nanjing 211169,China)(2.Purdue University Fort Wayne,Fort Wayne 46805,USA)
关键词:
赫曼德尔L2方法; 加权希尔伯特空间; 微分算子
Keywords:
Hormander L2 method; weighted Hilbert space; differential operator
分类号:
O177.92
DOI:
10.3969/j.issn.1001-4616.2020.03.002
文献标志码:
A
摘要:
本文利用复分析中研究柯西黎曼方程的赫曼德尔L2方法,研究了加权希尔伯特空间L2(R2,e-|x|2)上的微分算子Δ2+a,证明了由该算子所构成的微分方程的整体弱解的存在性,并证明了该算子的右逆有界算子的存在性.
Abstract:
Using Hormander L2 method for Cauchy-Riemann equations from complex analysis,we study a simple differential operator Δ2+a in weighted Hilbert space L2(R2,e-|x|2). We prove the existence of global weak solutions of the equation about the differential operator and the existence of a right bounded inverse of the differential operator.

参考文献/References:

[1] HORMANDER L. L2 estimates and existence theorems for the operator[J]. Acta mathematica,1965,113:89-152.
[2]ADACHI K. Several complex variables and integral formulas[M]. Singapore:World Scientific Publishing Co. Pte. Ltd,2007:53-99.
[3]KRANTZ S G. Function theory of several complex variables[M]. 2nd ed. Rhode Island:American Mathematical Society,2001:175-194.
[4]EVANS L C. Partial differential equations[M]. Rhode Island:American Mathematical Society,1998:23-25.
[5]DAI S Y,LIU Y,PAN Y F. A right inverse of differential operator Δ+a in weighted Hilbert space L2(Rn,e-|x|2)[J/OL]. Arxive-prints,2019:1909.12477v1.

备注/Memo

备注/Memo:
收稿日期:2020-04-17.
基金项目:国家自然科学基金项目(11671361).
通讯作者:戴绍虞,博士,副教授,研究方向:多复变函数论. E-mail:dymdsy@163.com
更新日期/Last Update: 2020-09-15