A local maximum principle for locally integrable structures

Let [Formula: see text] be an open subset, for a positive integer [Formula: see text], and let [Formula: see text] be a [Formula: see text]-smooth locally integrable subbundle. We give a proof of the following result: If [Formula: see text] is nowhere strictly hypoanalytically pseudoconvex (as defined in the paper) then for any sufficiently small domain [Formula: see text] and any [Formula: see text] which is continuous up to the boundary such that [Formula: see text] is a solution with respect to [Formula: see text] on [Formula: see text], it holds true that [Formula: see text] We also point out a relation to Levi curvature.