K(n)-localization of the K(n+1)-local E_n+1-Adams spectral sequences

We construct a spectral sequence converging to the homotopy set of maps from a spectrum to the K(n)-localization of the K (n + 1)-local sphere. We also construct a map of spectral sequences from the K(n)-local E_n-Adams spectral sequence to the preceding one. Then we compare the map on E₂-terms with a map induced by the inflation maps of continuous cohomology groups for Morava stabilizer groups. As an application we show that ζ_n in π_-1(L_K(n)S⁰) represented by the reduced norm map in the K (n)-local E_n-Adams spectral sequence has a nontrivial image under the map π_* (L_K(n)S⁰) → π_* (L_K(n)L_K(n+1)S⁰).