Hairer’s multilevel Schauder estimates without regularity structures

We investigate the regularising properties of singular kernels at the level of germs, i.e. families of distributions indexed by points in R d 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.