论文标题
Dirichlet系列的Hardy空间的乘数
Multipliers for Hardy spaces of Dirichlet series
论文作者
论文摘要
我们将乘数从Dirichlet系列的Hardy Space $ \ MATHCAL H_P $中的乘数表征为$ \ MATHCAL H_Q $，每$ 1 \ leq p，q \ leq \ leq \ infty $。对于固定的Dirichlet系列，我们还研究了其相关乘法运算符的某些结构特性。特别是，我们研究了这种操作员的规范，基本规范和频谱。我们利用了Dirichlet系列空间的现有自然识别，该空间在无限的许多变量中具有霍明型功能的空间，并应用了复杂和谐波分析中的几种方法来获得我们的结果。作为副产品，我们在这种庞大的尸体函数空间上获得了类似的陈述。
We characterize the space of multipliers from the Hardy space of Dirichlet series $\mathcal H_p$ into $\mathcal H_q$ for every $1 \leq p,q \leq \infty$. For a fixed Dirichlet series, we also investigate some structural properties of its associated multiplication operator. In particular, we study the norm, the essential norm, and the spectrum for an operator of this kind. We exploit the existing natural identification of spaces of Dirichlet series with spaces of holomorphic functions in infinitely many variables and apply several methods from complex and harmonic analysis to obtain our results. As a byproduct we get analogous statements on such Hardy spaces of holomorphic functions.
