Analysis in Theory and Applications

, Volume 20, Issue 4, pp 342–349

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

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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 hrp(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∈hrp(Ω) is obtained, where n/(n+1)<p≤1.

Key words

local Hardy space Green function convex domain potential estimate 

AMS(2000) subject classification

35J05 31C15 

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Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Department of MathematicsSouth-China Normal UniversityGuangzhouP. R. China
  2. 2.Department of MathematicsZhejiang UniversityHangzhouP. R. China

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