An application of regularly varying functions (Q1293398)

The authors prove that the conditions which are necessary for a convolution operator \(S\) in \({\mathcal K}_M'\) to be hypoelliptic are sufficient also, provided that the function is regularly varying at zero and infinity with positive indices of variation. Basic facts about the space \({\mathcal K}_M'\) and the space \({\mathcal O}_c' ({\mathcal K}_M',{\mathcal K}_M')\) of convolution operators \({\mathcal K}_M'\) are given together with some properties of regularly varying functions, and the main result is proved in the concluding section.