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Discrete Hölder estimates for a parametrix variation

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Abstract

In nonhomogeneous Hölder spaces, we prove continuity of integral operators with kernels from a special class and indicate simplest properties of this class. A parametrix of new type is constructed in a half-space for second order elliptic operators. We establish that, in local Hölder norms, it admits more exact estimate than that for a parametrix close to the Levi function.

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References

  1. M. Bramanti “Singular integrals in nonhomogeneous spaces: L2 and Lp continuity from Hölder estimates,” Rev. Mat. Iberoam. 26, 347 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Christ Lectures on Singular Integral Operators, CBMS Regional Conf. Ser. Math., 77, Providence, RI: AMS, 1990.

    Google Scholar 

  3. G. C. Hsiao and W. L. Wendland Boundary Integral Equations, Appl. Math. Sci. 164, Berlin: Springer-Verlag, 2008.

    Book  MATH  Google Scholar 

  4. H. Kalf, “On E. E. Levi’s method of constructing a fundamental solution for second-order elliptic equations,” Rend. Circ. Mat. Palermo (2) 41, 251 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. Meyer, “Continuitésur les espaces de Hölder et de Sobolev des opérateurs définis par des intégrales singulieres,” Recent Progress in Fourier Analysis (El Escorial, 1983), North-Holland Math. Stud., N111. Amsterdam: lsevier, 1985. P. 145–172.

    Google Scholar 

  6. S. G.Mikhlin and S. Prössdorf Singular Integral Operators. Berlin: Springer-Verlag, 1986.

    Book  Google Scholar 

  7. C. Miranda, Partial Differential Equations of Eliptic Type, Moscow: Inostrannaya Literatura DOI, 1957.

    Google Scholar 

  8. A. I. Parfenov, “Weighted a priori estimate in straightenable domains of local Lyapunov-Dini type,” Siberian Elect.Math. Rep. 9, 65 (2012) [in Russian].

    MathSciNet  Google Scholar 

  9. A. I. Parfenov, “Error bound for a generalized M. A. Lavrentiev’s formula via the norm in a fractional Sobolev space,” 10, 335 (2013) [in Russian].

    MathSciNet  Google Scholar 

  10. A. Pomp The Boundary-Domain Integral Method for Elliptic Systems. With an Application to Shells, Lecture Notes inMath., N1683. Berlin: Springer, 1998.

    MATH  Google Scholar 

  11. R. H. Torres Boundedness Results for Operators with Singular Kernels on Distribution Spaces, Mem. Amer.Math. Soc., V. 90, N442. Providence: AMS, 1991.

    MATH  Google Scholar 

  12. A. V. Vähäkangas Boundedness of Weakly Singular Integral Operators on Domains, Ann. Acad. Sci. Fenn.Math. Diss., N153. Helsinki: Univ. Helsinki, 2009.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. I. Parfenov

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  1. A. I. Parfenov
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Correspondence to A. I. Parfenov.

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Original Russian Text © A.I. Parfenov, 2014, published in Matematicheskie Trudy, 2014, Vol. 17, No. 1, pp. 175–201.

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Parfenov, A.I. Discrete Hölder estimates for a parametrix variation. Sib. Adv. Math. 25, 209–229 (2015). https://doi.org/10.3103/S1055134415030062

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  • DOI: https://doi.org/10.3103/S1055134415030062

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