一类积分算子的有界性

The boundedness of a class of integral operators

研究在单位圆盘加权空间L^(p)(D,dμ_(c))到L^(p)(D,dμ_(d))上的一类积分算子的有界性.通过不同的测试函数去寻找一类积分算子的有界性的必要条件.发现这类积分算子和其共轭算子之间的关系,得到一类积分算子的共轭算子有界的必要条件,从而简化证明.再通过舒尔检验去得到这类积分算子有界性的充分条件,从而得到这类积分算子有界性的完全刻画.

In this paper,we consider the boundedness of a class of integral operators over the unit disk from weighted space L^(p)(D,dμ_(c))into L^(p)(D,dμ_(d)).We use different test functions to seek the necessary conditions for the boundedness of a class of integral operators.We find the relationship between this class of integral operators and their adjoint operators and get the necessary condition for the boundedness of the adjoint operators of this kind of integral operators,so as to simplify the proof.Then we get the sufficient conditions for the boundedness of this class of integral operators by Schurs test.Hence we get the necessary and sufficient conditions for the boundedness of this class of integral operators.