论文标题
Toeplitz内核和向后移动
Toeplitz kernels and the backward shift
论文作者
论文摘要
在本文中，我们以$ 1 <p <\ infty $为$ 1 <p <\ infty $，研究标量和矢量价值的Hardy空间的Toeplitz运营商的内核。我们显示了矢量值Harty空间的任何元素的最小内核的存在，并确定了相应的Toeplitz运算符的符号。在标量情况下，我们对给定Toeplitz内核的最大功能进行了明确描述。在矢量案例中，我们显示并非所有toeplitz内核都具有最大功能，在$ p = 2 $的情况下，我们找到了toeplitz内核具有最大函数时的确切条件。对于标量和矢量价值的hardy空间，我们研究了包含Hardy空间中多个元素的最小toeplitz内核，我们还发现了Smirnov类中的功能的等效条件，以使后移循环。
In this paper we study the kernels of Toeplitz operators on both the scalar and the vector-valued Hardy space for $ 1 < p < \infty $. We show existence of a minimal kernel of any element of the vector-valued Hardy space and we determine a symbol for the corresponding Toeplitz operator. In the scalar case we give an explicit description of a maximal function for a given Toeplitz kernel. In the vectorial case we show not all Toeplitz kernels have a maximal function and in the case of $p=2$ we find the exact conditions for when a Toeplitz kernel has a maximal function. For both the scalar and vector-valued Hardy space we study the minimal Toeplitz kernel containing multiple elements of the Hardy space, we also find an equivalent condition for a function in the Smirnov class to be cyclic for the backwards shift.
