ELIMINATION OF L(1) SINGULARITIES FOR CR FUNCTIONS

For a closed subset S of a CR manifold M the relation (1) below is inv estigated. This is proved to hold when S is the characteristic set of M if this last does not contain an everywhere dense family of characte ristic manifolds of maximal dimension; in this case one can also take S as a peak set of a Holder CR function (theorem 2'). For connected re al analytic M, the non density assumption above is always verified unl ess M is everywhere characteristic. A simple example shows that even f or a C infinity pseudoconvex hypersurface in C2 and a thin peak set S of a smooth peak function, (1) is violated if the non density assumpti on is not fullfilled (theorem 4).