F. Bouchut et L. Desvillettes, A PROOF OF THE SMOOTHING PROPERTIES OF THE POSITIVE PART OF BOLTZMANNS KERNEL, Revista matematica iberoamericana, 14(1), 1998, pp. 47-61
We give two direct proofs of Sobolev estimates for the positive part o
f Boltzmann's kernel. The first deals with a cross section with separa
ted variables; no derivative is needed in this case. The second is con
cerned with a general cross section having one derivative in the angul
ar variable.