Interpolation in a generalized strip

It is shown that the description of interpolation sets for analytic Hölder classes in a standard strip can be carried over entirely to the generalized strip, i.e., to the subset of the standard strip bounded by two Lavrent'ev curves. To do this, some geometric properties of a generalized strip are established, namely, it is shown that a generalized strip can be extended accross the arcs of an interpolation set on the boundary, and that it decomposes in Lavrent'ev domains.