  The main purpose of this work is to establish some logarithmic estimates of
optimal type in the Hardy-Sobolev space $H^{k, \infty}; k \in {\mathbb{N}}^*$
of an annular domain. These results are considered as a continuation of a
previous study in the setting of the unit disk by L. Baratchart and M. Zerner:
On the recovery of functions from pointwise boundary values in a Hardy-sobolev
class of the disk. J.Comput.Apll.Math 46(1993), 255-69 and by S. Chaabane and
I. Feki: Logarithmic stability estimates in Hardy-Sobolev spaces
$H^{k,\infty}$. C.R. Acad. Sci. Paris, Ser. I 347(2009), 1001-1006.
  As an application, we prove a logarithmic stability result for the inverse
problem of identifying a Robin parameter on a part of the boundary of an
annular domain starting from its behavior on the complementary boundary part.
