Abstract

We consider a class of ultraparabolic differential equations that satisfy the Hörmander's hypoellipticity condition and we prove that the weak solutions to the equation with measurable coe±cients are locally bounded functions. The method extends the Moser's iteration procedure and has previously been employed in the case of operators verifying a further homogeneity assumption. Here we remove that assumption by proving some potential estimates and some ad hoc Sobolev type inequalities for solutions.