@article {Astashkin:July 2006:0016-2663:218, author = "Astashkin, S.", author = "Sunehag, P.", title = "The real interpolation method on couples of intersections", journal = "Functional Analysis and Its Applications", volume = "40", year = "July 2006", abstract = "Suppose that (X 0, X 1) is a Banach couple, X 0X 1 is dense in X 0 and X 1, (X0,X1)θq (0 < θ < 1, 1 ≤ q < ∞) are the spaces of the real interpolation method, ψ ∈ (X 0X 1), ψ ≠ 0, is a linear functional, N = Ker ψ, and N i stands for N with the norm inherited from X i (i = 0, 1). The following theorem is proved: the norms of the spaces (N0,N1)θ,q and (X0,X1)θ,q are equivalent on N if and only if θ   (0, α) ∪ (β, α0 ∪ (β0, α) ∪ (β, 1), where α, β, α0, β0, α, and β are the dilation indices of the function k(t)=k(t,ψ;X 0 * ,X 1 * ).", pages = "218-221(4)", url = "http://www.ingentaconnect.com/content/klu/faia/2006/00000040/00000003/00000033" doi = "doi:10.1007/s10688-006-0033-0" }