Pointwise estimates for degenerate Kolmogorov equations with $$L^p$$-source term

The aim of this paper is to establish new pointwise regularity results for solutions degenerate second-order partial differential equations with a Kolmogorov-type operator the form $$\begin{aligned} {\mathscr {L}}:=\sum _{i,j=1}^m \partial ^2_{x_i x_j } +\sum _{i,j=1}^N b_{ij}x_j\partial _{x_i}-\partial _t, \end{aligned}$$ where $$(x,t) \in {{\mathbb {R}}}^{N+1}$$ , $$1 \le m N$$ and matrix $$B:=(b_{ij})_{i,j=1,\ldots ,N}$$ has real constant entries. In particular, we show that if modulus $$L^p$$ -mean oscillation $${\mathscr {L}}u$$ at origin Dini, then Lebesgue point continuity in average derivatives $$\partial x_j} u$$ $$i,j=1,\ldots ,m$$ Lie derivative $$\left( \sum _t\right) . Moreover, are able provide Taylor-type expansion up second order an estimate rest norm. proof based on decay estimates, which achieve by contradiction, blow-up compactness results.