Hardy Space of Exact Forms on R

Abstract

We show that the Hardy space of divergence-free vector fields on R3 has a divergence-free atomic decomposition, and thus we characterize its dual as a variant of BMO. Using the duality result we prove a “div-curl” type theorem: for b in Lloc(R 3,R3), sup ∫ b · (∇u×∇v) dx is equivalent to a BMOtype norm of b, where the supremum is taken over all u, v ∈ W 1,2… (More)

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