If X satisfies div(L^∞ ∩ X) = div X, then the real interpolation spaces (L^∞, X)_{θ,q} also satisfy this equality for θ in (0,1) and q in [1,∞).
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Subspaces of A(D)-free elements in X^N, for X in {W^{l,1}(T^d), W^{l,∞}(T^d), C^l(T^d)} with d≥2, are noncomplemented for appropriate N×N matrix operators A(D).
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Bourgain-Brezis spaces obtained by real interpolation
If X satisfies div(L^∞ ∩ X) = div X, then the real interpolation spaces (L^∞, X)_{θ,q} also satisfy this equality for θ in (0,1) and q in [1,∞).
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Nonexistence of Henkin type projections via a Wiener theorem for multipliers
Subspaces of A(D)-free elements in X^N, for X in {W^{l,1}(T^d), W^{l,∞}(T^d), C^l(T^d)} with d≥2, are noncomplemented for appropriate N×N matrix operators A(D).