The transformations in question are generalizations of the matrix transformations of summability theory. Let K(u) be the Knopp kernel of the function u, and say that an operator A generates an embedding of kernels (or embedding of bounded kernels) if for every x (or bounded x) K(A(x))\(\subset K(x)\). Theorem 1: a linear regular operator A generates an embedding of bounded kernels if and only if \(\| A\| =1\) (where \(\| A\| =\inf \{c\geq 0,\| A(x)\| \leq c\| x\| \}\) and \(\| x\| = \limsup| x(s)|)\). An operator A has property (K) if for every x such that \(0\in K(A(x))\) there is a function \(z(s)\to +\infty\) such that \(0\in K(A(zx))\). Theorem 2. Every regular matrix has property (K) on the space of sequences to which it applies. An operator A is strongly regular if \(K(x)=\{a\}\) implies \(K(A(x))=\{a\}\). Theorem 3. Every strongly regular operator A with property (K) generates an embedding of kernels.