  We establish the boundedness of weak subsolutions for a class of degenerate
Kolmogorov equations of hypoelliptic type, compatible with a homogeneous Lie
group structure, within bounded product domains using the De Giorgi iteration.
We employ the renormalization formula to handle boundary values and provide
energy estimates. An $L^1$-$L^p$ type embedding estimate derived from the
fundamental solution is utilized to incorporate lower-order divergence terms.
This work naturally extends the boundedness theory for uniformly parabolic
equations, with matching exponents for the coefficients.
