Lᵖ-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials

We establish a priori estimates showing the propagation and generation of Lᵖ-norms for solutions to the non-cutoff spatially homogeneous Boltzmann equation with soft potentials. The singularity of the collision kernel is key to generate regularization and inhomogeneity in the energy estimates of the Lᵖ-norms. Our result extends Alo19 from the hard potential cases to the soft ones.