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Singular Integrals and Fourier Multipliers on Infinite Lipschitz Curves

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Singular Integrals and Fourier Theory on Lipschitz Boundaries
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Abstract

The main contents of this chapter are closely related with harmonic analysis and operator theory. Let \(\gamma \) denote a Lipschitz graph on the complex plane \(\mathbb C\).

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References

  1. McIntosh A, Qian T. Convolution singular integral operators on Lipschitz curves, in Lecture Notes in Math. 1494, Springer, 1991;142–162.

    Google Scholar 

  2. McIntosh A, Qian T, Fourier theory on Lipschitz curves. Minicoference on Harmonic Analysis, Proceedings of the Center for Mathematical Analysis. ANU, Canberra;1987 (15):157–166.

    Google Scholar 

  3. McIntosh A, Qian T. \(L^{p}\) Fourier multipliers on Lipschitz curves. Center for Mathematical Analysis Research Report, R36-88, ANU, Canberra;1988.

    Google Scholar 

  4. McIntosh A, Operators which have an \(H_{\infty }-\)functional calculus. Miniconference on Operator Theory and Partial Differential Equations. In: Proceedings of the Center for Mathematical Analysis, ANU. Canberra. 14:1986.

    Google Scholar 

  5. Kenig C. Weighted \(H^{p}\) spaces on Lipschitz domains. Amer. J. Math. 1980;102:129–63.

    Article  MathSciNet  Google Scholar 

  6. Coifman R, Meyer Y. Au-delá des opérateurs pesudo-différentiels. Astérisque, 57, Societe Mathématique de France, 1978.

    Google Scholar 

  7. McIntosh A, Qian T. Fourier multipliers on Lipschitz curves. Trans. Amer. Math. Soc. 1992; p. 157–176.

    Google Scholar 

  8. McIntosh A, Qian T. A note on singular integrals with holomorphic kernels. Approx. Theory Appl. 1990;6:40–57.

    MathSciNet  MATH  Google Scholar 

  9. Calderón CP. Cauchy integrals on Lipschitz curves and related operators. Proc. Nat. Acad. Sc. USA. 1977;74:1324–7.

    Article  MathSciNet  Google Scholar 

  10. Coifman R, McIntosh A, Meyer Y. L’integral de Cauchy définit un opérateur borné sur \(L^{2}\) pour les courbes Lipschitziennes. Ann. Math. 1982;116:361–87.

    Article  MathSciNet  Google Scholar 

  11. Coifman R, Meyer Y. Fourier analysis of multilinear convolutions, Calderón’s theorem, and analysis on Lipschitz curves. Lecture Notes in Mathematica, 779, 104–122, Springer, Berlin, 1980.

    Google Scholar 

  12. Jones P., Semmes S. An elementary proof of the \(L^{2}\) boundedness of Cauchy integrals on Lipschitz curves, preprint.

    Google Scholar 

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Qian, T., Li, P. (2019). Singular Integrals and Fourier Multipliers on Infinite Lipschitz Curves. In: Singular Integrals and Fourier Theory on Lipschitz Boundaries. Springer, Singapore. https://doi.org/10.1007/978-981-13-6500-3_1

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