We consider kernels of unbounded Toeplitz operators in $H^p(\mathbb C^+)$ in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in $H^p(\mathbb C^+)$, we describe the kernels of Toeplitz operators whose symbol possesses a certain factorization involving two different Hardy spaces and we establish relations between the kernels of two operators whose symbols differ by a factor which corresponds, in the unit circle, to a non-integer power of $z$. We apply the results to describe the kernels of Toeplitz operators with non-vanishing piecewise continuous symbols.

中文翻译：

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无界托普利兹算子的核和符号的因式分解

我们根据符号的因式分解考虑 $H^p(\mathbb C^+)$ 中无界 Toeplitz 算子的核。我们研究了包含 $H^p(\mathbb C^+)$ 中给定函数的最小托普利兹核的存在性，我们描述了托普利兹算子的核，其符号具有涉及两个不同哈代空间的特定分解，并建立了之间的关系两个运算符的内核，其符号相差一个因子，在单位圆中对应于 $z$ 的非整数幂。我们应用结果来描述具有非消失分段连续符号的 Toeplitz 算子的核。