We characterize the reproducing kernel Hilbert spaces whose elements are$p$-integrable functions in terms of the boundedness of the integral operatorwhose kernel is the reproducing kernel. Moreover, for $p=2$ we show that thespectral decomposition of this integral operator gives a complete descriptionof the reproducing kernel.
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机译：我们以其为重现内核的积分算子的有界性为特征，描述了重现内核希尔伯特空间，其元素是$ p $可积分函数。此外，对于$ p = 2 $，我们证明了该积分算子的谱分解给出了再现核的完整描述。
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