POTENTIAL SPACE ESTIMATES IN LOCAL HARDY SPACES FOR GREEN POTENTIALS IN CONVEX DOMAINS

摘要

Let Ω be a bounded convex domain in R~n(n ≥ 3) and G(x,y) be the Green function of the Laplace operator -Δ on Ω. Let h_r~p(Ω) = { f ∈D′(Ω) : exist F ∈ h~p(R~n), s.t. F|_Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f → ▽~2(Gf) for every f ∈ h_r~p(Ω) is obtained, where n/(n + 1) < p ≤ 1.