Journal of Integral Equations and Applications

On the Analyticity of the Cauchy Integral in Schauder Spaces

Massimo Lanza de Cristoforis and Luca Preciso

Full-text: Open access

Article information

Source
J. Integral Equations Applications Volume 11, Number 3 (1999), 363-391.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1181074283

Digital Object Identifier
doi:10.1216/jiea/1181074283

Mathematical Reviews number (MathSciNet)
MR1719083

Zentralblatt MATH identifier
0987.47022

Citation

Cristoforis, Massimo Lanza de; Preciso, Luca. On the Analyticity of the Cauchy Integral in Schauder Spaces. J. Integral Equations Applications 11 (1999), no. 3, 363--391. doi:10.1216/jiea/1181074283. https://projecteuclid.org/euclid.jiea/1181074283


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References

  • M.S. Berger, Nonlinearity and functional analysis, Academic Press, New York, 1977.
  • A.P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Natl. Acad. Sci. U.S.A. 74 (1977), 1324-1327.
  • R.R. Coifman, A. McIntosh and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur $L^2$ pour les courbes lipschitziennes, Ann. of Math. 116 (1982), 361-387.
  • R.R. Coifman and Y. Meyer, L'analyse armonique non linéaire, in Proc. of a seminar held in Turin and Milan in 1982: Topics on modern harmonic analysis (De Leonida-Ricci, ed.), INDAM F. Severi, Roma, 2 1983, 707-721.
  • --------, Lavrentiev's curves and conformal mappings, Report No. 5 -1983.
  • G. David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. 4$^\rm e$ série 17 (1984), 157-189.
  • C. Godbillon, Éléments de topologie algébrique, Hermann, Paris, 1971.
  • E. Hille and R.S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ. 31 (1957).
  • W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press, Princeton, 1948.
  • P. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), 71-88.
  • J.L. Journé, Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón, Lecture Notes in Math. 994, Springer-Verlag, New York, 1983.
  • A. Kufner, O. John and S. Fučík, Function spaces, Noordhoff Internat. Publ., Leyden, 1977.
  • M. Lanza de Cristoforis, Properties and pathologies of the composition and inversion operators in Schauder spaces, Acc. Naz. delle Sci. detta dei XL 15 (1991), 93-109.
  • --------, Differentiability properties of an abstract autonomous composition operator, 1996 (submitted).
  • --------, A functional decomposition theorem for the conformal representation, J. Math. Soc. Japan 49 (1997), 759-780.
  • M. Lanza de Cristoforis and S.S. Antman, The large deformation of nonlinearly elastic tubes in two-dimensional flows, SIAM J. Math. Anal. 22 (1991), 1193-1221.
  • M. Lanza de Cristoforis and S.V. Rogosin, Analyticity of a nonlinear operator associated to the conformal representation in Schauder spaces. An integral equation approach, 1997 (submitted).
  • J.K. Lu, Boundary value problems for analytic functions, World Scientific, Singapore, 1993.
  • Y. Meyer and R.R. Coifman, Ondelettes et opérateurs, vol. III, Éditeurs des Sciences et des Arts, Hermann, Paris, 1991.
  • N.I. Muskhelishvili, Singular integral equations, Groningen-Holland, 1953.
  • G. Prodi and A. Ambrosetti, Analisi non lineare, Editrice tecnico scientifica, Pisa, 1973.
  • C. Tran-Oberlé, Analyse non linéaire de l'opérateur défini par l'intégrale de Cauchy, Bull. Soc. Math. France 117 (1989), 1-18.
  • G.M. Troianiello, Elliptic differential equations and obstacle problems, Plenum Publishing Co., New York, 1987.
  • I.N. Vekua, Generalized analytic functions, Pergamon Press, New York, 1962.
  • S. Wu, Analytic dependence of Riemann mappings for bounded domains and minimal surfaces, Comm. Pure Appl. Math. 46 (1993), 1303-1326.