Bounds for Characteristic Functions of Certain Degenerate Multidimensional Distributions

Probability distribution concentrated on $k$-dimensional smooth surfaces in $R^m$ are shown to possess characteristic functions which decrease like negative powers of the norm of their argument (the latter tending to infinity) if they are generated by bounded surface densities satisfying a Lipschitz condition and the surface (support of the distribution) has no contacts of arbitrarily high order with $(m-1)$-dimensional hyperplanes in $R^m$.