A note on asymptotical estimates for the rate of decrease at infinity of the eigenfunctions of integral operators

The article is devoted to the problem of finding estimates of the rate of decrease at infinity of the eigenfunctions of integral operators. A class of integral operators that admit majorant operators, defined by a certain sublinear function $S(x)$, is introduced. It is shown that all eigenfunctions of operators from this class admit a universal estimate for the rate of decrease at infinity which includes the function $S(x)$. The applications of the obtained result to integral equation typical for mathematical physics are discussed.