We extend the results of Pollard [4] and give asymptotic estimates for the norm of the Fourier-Gegenbauer projection operator in the appropriate weighted L-p space. In particular, we settle the question of whether the projection is bounded for p = (2 lambda + 1)/lambda and p = (2 lambda + 1)/(lambda + 1), where lambda is the index for the family of Gegenbauer polynomials under consideration.153369379