Square-integrable kernel

Summary

A square-integrable kernel is a kernel $K(x, s)$ whose squared absolute value has a finite double integral. Such kernels are also called Hilbert–Schmidt kernels or $L^2$ kernels. The integral operator of a square-integrable kernel is a bounded and compact operator on the Lp space $L^2$, namely a Hilbert–Schmidt integral operator. This class contains all continuous kernels on a square and also many unbounded ones.