Topologically invariant ϕ-means and uniformly continuous functionals on the dual of the Lebesgue-Fourier algebra related to coset spaces

Let K be a compact subgroup of a locally compact group G. We investigate topologically invariant ?-means (with norm one) over the dual of the Lebesgue-Fourier algebra related to coset spaces G/K, where ? is a nonzero character of the Lebesgue-Fourier algebra on G/K. We prove that the set of all topologically invariant ?-means over dual of the Fourier algebra of G/K and the set of all topologically invariant ?-means over the dual of the Lebesgue-Fourier algebra of G/K have the same cardinality. Furthermore, we introduce and study the spaces weakly almost periodic functionals and uniformly continuous functionals over the Lebesgue-Fourier algebra of G/K.