Skip to main content
SpringerLink
Log in

Boundary Value Problems for Analytic Functions with Boundary Data from Grand Lebesgue Spaces

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We study solutions of the Riemann boundary value problem in the class of Cauchy type integrals with densities from grand Lebesgue spaces in domains with nonsmooth boundaries. The case of piecewise conjugacy coefficients is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. I. Muskhelishvili, Singular Integral Equations, Wolters-Noordhoff, Gröningen (1967).

    MATH  Google Scholar 

  2. N. I. Muskhelishvili, Singular Integral Equations. Boundary Problems of Function Theory and Their Applications to Mathematical Physics, Melbourne (1949).

  3. T. Iwaniec and C. Sbordone, “On the integrability of the Jacobian under minimal hypotheses,” Arch. Ration. Mech. Anal. 119, No. 2, 129–143 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Greco, T. Iwaniec, and C. Sbordone, “Inverting the p-harmonic operator,” Manuscr. Math. 92, No. 2, 249–258 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Khuskivadze, V. Kokilashvili, and V. Paatashvili, “Boundary value problems for analytic and harmonic functions in domains with nonsmooth boundaries. Applications to conformal mappings,” Mem. Differ. Equ. Math. Phys. 14, 1–195 (1998).

    MathSciNet  MATH  Google Scholar 

  6. G. David, “Opérateurs intégraux singuliers sur certaines courbes du plan complexe,” Ann. Sci. Éc. Norm. Supér. (4) 17, 157–189 (1984).

    Article  MATH  Google Scholar 

  7. A. Fiorenza and V. Kokilashvili, “Nonlinear harmonic analysis integral operators in weighted grand Lebesgue spaces and applications,” Ann. Funct. Anal. 9, No 3, 413–425 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  8. V. Kokilashvili, “Boundedness criteria for singular integrals in weighted grand Lebesgue spaces,” J. Math. Sci. 170, No. 1, 20–33 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Böttcher and Y. I. Karlovich, Carleson Curves, Muckenhoupt Weights and Toeplitz Operators, Bikrhäuser, Basel etc. (1997).

  10. V. P. Havin, “Boundary properties of Cauchy type integrals and harmonically conjugated functions in domains with rectifiable boundary” [in Russian], Mat. Sb. 68, No. 4, 499–517 (1965).

  11. B. V. Khvedelidze, “The method of Cauchy type integrals for discontinuous boundary value problems of the theory of holomorphic functions of one complex variable,” J. Math. Sci. 7, 309–414 (1977).

    Article  MATH  Google Scholar 

  12. G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Am. Math. Soc., Providence, RI (1969).

Download references

Author information

Authors and Affiliations

  1. A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2, Merab Aleksidze II Lane, 0193, Tbilisi, Georgia

    V. Kokilashvili

Authors
  1. V. Kokilashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Kokilashvili.

Additional information

Dedicated to the 85th birthday of Professor V. Maz’ya

Translated from Problemy Matematicheskogo Analiza 118, 2022, pp. 97-107.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kokilashvili, V. Boundary Value Problems for Analytic Functions with Boundary Data from Grand Lebesgue Spaces. J Math Sci 268, 355–367 (2022). https://doi.org/10.1007/s10958-022-06200-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-06200-4

Search

Navigation