  We investigate the regularising properties of singular kernels at the level
of germs, i.e. families of distributions indexed by points in $\mathbb{R}^d$.
First we construct a suitable integration map which acts on general coherent
germs. Then we focus on germs that can be decomposed along a basis
(corresponding to the so-called modelled distributions in Regularity
Structures) and we prove a version of Hairer's multilevel Schauder estimates in
this setting, with minimal assumptions.
