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

Analysis in Theory and Applications

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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References

  1. Chang, D. C., Krantz, S. G. and Stein, E. M.,H p Theory on a Smooth domain inR N and Elliptic Boundary Value Problems, J. Funct. Anal., 114(1993), 286–347.

    Article  MATH  MathSciNet  Google Scholar 

  2. Grisvard, P., Elliptic Problems in Nonsmooth Domains, Pitman, Boston, MA, 1985.

    MATH  Google Scholar 

  3. Adolfsson, V.,L p-Integrability of the Second Order Derivatives of Green Potentials in Convex Domains, Pacific J. Math., 159:2(1993), 201–225.

    MATH  MathSciNet  Google Scholar 

  4. Fromm, S. J., Potential Spaces Estimates for Green Potentials in Convex Domains, P. A. M. S., 119:1(1993), 225–233.

    Article  MATH  MathSciNet  Google Scholar 

  5. David, G., A Local Version of Real Hardy Spaces, Duke. Math., 46:1(1979), 27–42.

    Article  MATH  MathSciNet  Google Scholar 

  6. Gruter, M. and Widman, K. O., The Green Function for Uniformly Elliptic Equations, Manuscripta Math., 37(1982), 303–342.

    Article  MathSciNet  Google Scholar 

  7. Stein, E. M., Singular Integals and Differentialbility Properties of Functions, Princenton University, New Jersey, 1970.

    Google Scholar 

  8. Miyachi, A.,H p Space Over Open Subsets ofR n, Studia Math., 95(1990), 205–228.

    MathSciNet  Google Scholar 

  9. Bergh, J. and Lofstrom, J., Interpolation Spaces An introduction, Grund. Math. Wissen. 223, 1996.

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Correspondence to Wang Henggeng.

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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

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