Hardy space of exact forms on Rᴺ
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 Lloc2(ℝ 3, ℝ3), sup ∫ b · (∇u × ∇v) dx is equivalent to a BMO-type norm of 6, where the supremum is taken over all u, v ∈ W1,2(ℝ3) with ∥∇u∥L2, ∥∇v∥L2 ≤ 1. This theorem is used to obtain some coercivity results for quadratic forms which arise in the...[Show more]
|Collections||ANU Research Publications|
|Source:||Transactions of the American Mathematical Society|
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