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 Rd. 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.