<p>The note aims to extend the Bukhvalov theorem on the kernel representation of linear operators in spaces of measurable functions to the polynomial context. It is shown that every orthogonally additive homogeneous polynomial acting from a space of Bochner measurable functions with values in a Banach lattice to a space of weakly measurable vector-functions and dominated by a kernel operator is representable by means of weakly measurable operator-valued kernel.</p>