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We establish the Schauder estimates at the boundary away from thecharacteristic points for the Dirichlet problem by means of the double layerpotential in a Heisenberg-type group $\mathbb{G}$. Despite its singularity wemanage to invert the double layer potential restricted to the boundary thanksto a reflection technique for an approximate operator in $\mathbb{G}$. This isthe first instance where a reflection-type argument appears to be useful in thesub-Riemannian setting.

Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential