从Bergman空间到Bloch空间的叠加算子

Superposition Operators from the Bergman Space to Bloch Space

研究从Bergman空间到Bloch空间的叠加算子.从函数空间的性质出发,利用不同维数的函数空间之间的关系,讨论叠加算子,把单变量有关叠加算子的结果推广到多变量,得到了与单变量一致的结果,从而刻画了从Bergman空间到Bloch空间的叠加算子的特征,得到了从Bergman空间到Bloch空间的叠加算子的充要条件.

We research the superposition operators from the Bergman space to Bloch space. With the nature of function spaces and the relationship between the function spaces of different dimensions, we discuss the superposition operators, generalize the results of superposition operator about single variable to multiple variables and obtain the results that are consistent with the ones of single variable. It describes the nature and obtains necessary and sufficient conditions of the superposition operators from the Bergman space to Bloch space.