Uniqueness Theorems for CR Functions

Let M be a CR manifold embedded in ℭ s of arbitrary codimension. M is called generic if the complex hull of the tangent space in all points of M is the whole ℭ s . M is minimal (in sense of Tumanov) in p ϵ M if there does not exist any CR submanifold of M passing through p with the same CR dimension as M but of smaller dimension. Let M be generic and minimal in some point p ϵ M and N be a generic submanifold of M passing through p . We prove that a continuous CR function on M vanishes identically in some neigbourhood of p if its restriction to N either vanishes in p faster then some function with non‐integrable logarithm or it vanishes on a subset of N of positive measure.