关于微分算子Δ^2+a的一个注记

A Note on the Differential OperatorΔ^2+a

本文利用复分析中研究柯西黎曼方程的赫曼德尔L^2方法,研究了加权希尔伯特空间L^2(R^2,e-|x|2)上的微分算子Δ^2+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.

Using Hormander L^2 method for Cauchy-Riemann equations from complex analysis,we study a simple differential operatorΔ^2+a in weighted Hilbert space L^2(R^2,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.