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

Authors

    • Department of MathematicsSouth-China Normal University
  • Jia Houyu
    • Department of MathematicsZhejiang University
Article

DOI: 10.1007/BF02835227

Cite this article as:
Henggeng, W. & Houyu, J. Anal. Theory Appl. (2004) 20: 342. doi:10.1007/BF02835227
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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 spaceGreen functionconvex domainpotential estimate

AMS(2000) subject classification

35J0531C15

Copyright information

© Springer 2004