Orlicz空间内第一类不适定积分方程的解

The Solution of First Kind Ⅲ-Posed Integral Equations

讨论由L^2[a,b]到Orlicz空间L_M~*[a,b]内第一类积分方程 integral from n=a to b(K(x,y)g(y)dy=f(x)) (1)f∈L_M~*[a,b]。这里K(x,y)满足 integral from n=a to b integral from n=a to b(|K(x,y)|~2dxdy〈∞) L_M~*[a,b]为N函数M(u)生成的Orlicz空间,并赋以Orlicz范数||·||_M;L_(N)~*[a,b]为M(u)的余N函数N(v)生成的Orlicz空间,赋以Luxemburg范数。

In this paper, the problems for the solution to the first kind ill-posed in- tegral equations are studied. By introducing a new kernal function, the minimum norm so- lution to the ill--posed equation can be obtained from the solution to some well posed in- tegral equation.