Real Interpolation with Constraints Original Research Article

Given Banach spaces X, a subspace Y, and a finite set G of bounded linear functionals on Y, let YG denote all elements of Y which are annihilated by the functionals in G. We investigate the relation between the real interpolation spaces (X, Y)θ, ρ and (X, YG)θ, ρ. Applications are given to Sobolev spaces, best approximation with constraints, and weighted Lebesgue spaces.