Approximation by K-finite functions in Lp spaces

Let Gamma subset of R-n, n >= 2, be the boundary of a bounded domain. We prove that the translates by elements of Gamma of functions which transform according to a fixed irreducible representation of the orthogonal group from a dense class in L-p(R-n) for p >= 2n/n+1. A similar problem for noncompact symmetric spaces of rank one is also considered. We also study the connection of the above problem with the injective sets for weighted spherical mean operators.