调和Bergman空间上大Hankel算子性质的研究

Study on Properties of Big Hankel Operator on Harmonic Bergman Space

摘要: 本篇文章主要讨论了调和Bergman空间上以径向函数为符号的大Hankel算子的一些性质，构造了一个与其符号函数相关的数列{φ_k}，得到了一些有关大Hankel算子的性质的一些结论。其有界性与{φ_k}的有界性等价，其紧性与{φ_k}收敛到0等价，其正定性与{φ_k}为大于0的有界数列等价。

Abstract: This article mainly discusses some of the properties of the Big Hankel operator whose symbol is a radial function on the Bergman space. It constructs a series {φ_k} related to its symbolic function and obtains some conclusions about the nature of the big Hankel operator. The boundedness of the big Hankel operator is equivalent to the boundedness of {φ_k}. The compactness of the big Hankel operator converges to zero with {φ_k} , and the positivity of the big Hankel operator is equivalent to the bounded sequence with {φ_k}greater than zero.