标题： Hausdorff 算子在 de Branges 空间和 Paley-Wiener 空间上 显示英文标题

标题： Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces

摘要： 对于包含多项式的de Branges空间类，给出了所考虑的Hausdorff算子有界性和紧性的充分必要条件。 对于Paly-Wiener空间，我们将我们的Hausdorff算子的研究简化为经典的积分算子。 出现的算子是Carleman，因此在$L^2(\mathbb{R})$中是闭合的。 我们还获得了我们的算子在Paley-Wiener空间中有界性、紧性和核性的条件，以及它们属于Hilbert-Schmidt类的条件。 显示英文摘要

摘要： For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consideration. For the Paly-Wiener spaces we reduce the study of our Hausdorff operators to classical integral ones. The operators that appeared are Carleman and therefore closeble in $L^2(\mathbb{R})$. We obtain also conditions for boundedness, compactness and nuclearity of our operators in the Paley-Wiener space as well as the conditions for their belonging to the Hilbert-Schmidt class.