Bergman空间上拟齐次Toeplitz算子的乘积

摘要

This paper concerns with the product of Toeplitz operators on the Bergman space with symbols in the quasihomogeneous functions. Three cases in terms of the degree of the symbol are discussed. By using Mellin transform, the necessary and sufficient conditions are given for the product of two Toeplitz operators to be a Toeplitz operator. These results improve the previous ones.%使用Mellin变换作为工具,讨论了Bergman空间上以拟齐次函数为符号的Toeplitz算子的乘积问题,得出了当拟齐次函数的度处于三种不同情况时两个Toeplitz算子乘积仍是Toeplitz算子的充分必要条件.