Is there a difference between singular values of a kernel and its associated integral operator

Question

Suppose we have a square integrable kernel $K_A(s,t)$. Define the integral operator $A:H \rightarrow H_A$, where $H,H_A$ are Hilbert spaces, by $$Ah = \int_{\Omega_s}K_A(s,t)h(s)ds,$$ for all $h\in H$. Are the singular values of the kernel $K_A$ and the operator $A$ defined to be the same? I cannot find a conclusive answer. References are appreciated!