Decompositions of certain loop spaces

In this note we will study, for a space taken from two different classes of spaces, the decomposition of the loop space on such a space into atomic factors. The first class consists of certain mapping cones of maps between wedge products of Moore spaces. The second one is a p-local version of the class of coformal spaces from rational homotopy theory. As an application we verify Mooreʹs conjecture about homotopy exponents for these spaces.