Real interpolation of Hardy-type spaces and BMO-regularity

Abstract

Let (X, Y ) be a couple of quasi-Banach lattices of measurable functions on T × Ω satisfying some additional assumptions. The K-closedness of a couple of Hardy-type spaces (X A , Y A ) in (X, Y ) and the stability of the real interpolation (X A , Y A ) θ,p = (X A + Y A ) ∩ (X, Y ) θ,p are shown to be equivalent to each other and to the BMO-regularity of the associated lattices L 1 , (X r ) ′ Y r δ,q . The inclusionis also characterized in these therms. New examples of couples (X A , Y A ) with this stability are given, proving that this property is strictly weaker than the BMOregularity of (X, Y ).