Potential space estimates in local Hardy spaces for Green potentials in convex domains

Let Ω be a bounded convex domain in Rⁿ(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): ∃F∈h^p(Rⁿ),s.t. F|ω=f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound off→∇²(Gf) for every f∈h _r ^p (Ω) is obtained, where n/(n+1)<p≤1. Supported by the NSFC (No. 19971030, 10471050), Tianyuan Fund (No. 10426016) and the NFC of Guangdong (No. 031495).