Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), 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 ∈ hrp(Ω) is obtained, where n/(n + 1)<p≤1.
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机译:设Ω为Rn(n≥3)中的有界凸域,G(x,y)为Laplace算子-△的Green函数。令hrp(Ω)= {f∈D'(Ω):(E)F∈hp(Rn),s.t. F |Ω= f},通过在有界Lipschitz域中对局部Hardy空间进行原子刻画,得到每个f∈hrp(Ω)的f→(△)2(Gf)的界,其中n /(n + 1)<p≤1。
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