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This document presents an elementary approach using $\varepsilon$-Poincar\'einequality to prove generation of $L^{p}$-bounds, $p\in(1,\infty)$, for thehomogeneous Landau equation with moderate soft potentials $\gamma\in[-2,0)$.The critical case $\gamma=-2$ uses an interpolation approach in the realm ofLorentz spaces and entropy. Alternatively, a direct approach using theHardy-Littlewood-Sobolev (HLS) inequality and entropy is also presented. Onthis basis, the generation of pointwise bounds $p=\infty$ is deduced from a DeGiorgi argument.

The Landau equation with moderate soft potentials: An approach using $\varepsilon$-Poincar\'e inequality and Lorentz spaces