Abstract
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 pr (Ω)={f∈D′(Ω): ∃F∈hp(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 pr (Ω) is obtained, where n/(n+1)<p≤1.
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Supported by the NSFC (No. 19971030, 10471050), Tianyuan Fund (No. 10426016) and the NFC of Guangdong (No. 031495).
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Henggeng, W., Houyu, J. Potential space estimates in local Hardy spaces for Green potentials in convex domains. Anal. Theory Appl. 20, 342–349 (2004). https://doi.org/10.1007/BF02835227
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DOI: https://doi.org/10.1007/BF02835227