Am. Kytmanov et C. Rea, ELIMINATION OF L(1) SINGULARITIES FOR CR FUNCTIONS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 318(12), 1994, pp. 1093-1096
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).