Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves

 Access to full text

 Full (PDF)

1. [CM1] R. Coifman and Y. Meyer, Fourier analysis of multilinear convolutions, Calderón's theorem, and analysis on Lipschitz curves, in: Lecture Notes in Math. 779, Springer, 1980, 104-122. 
2. [CM2] R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57 (1978). Zbl0483.35082
3. [CMcM] R. Coifman, A. McIntosh et Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^2$ pour les courbes lipschitziennes, Ann. of Math. 116 (1982), 361-387. 
4. [D] G. David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. 17 (1984), 157-189. Zbl0537.42016
5. [DJS] G. David, J. L. Journé et S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), 1-56. Zbl0604.42014
6. [FJR] E. B. Fabes, M. Jodeit, Jr. and N. M. Rivière, Potential techniques for boundary value problems on $C^1$ domains, Acta Math. 141 (1978), 165-186. Zbl0402.31009
7. [GQW] G. Gaudry, T. Qian and S.-L. Wang, Boundedness of singular integral operators with holomorphic kernels on star-shaped Lipschitz curves, Colloq. Math. 70 (1996), 133-150. Zbl0860.42013
8. [LMcQ] C. Li, A. McIntosh and T. Qian, Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces, Rev. Mat. Iberoamericana 10 (1994), 665-721. Zbl0817.42008
9. [LMcS] C. Li, A. McIntosh and S. Semmes, Convolution singular integral operators on Lipschitz surfaces, J. Amer. Math. Soc. 5 (1992), 455-481. Zbl0763.42009
10. [Mc] A. McIntosh, Operators which have an $H_{\infty }$-functional calculus, in: Miniconference on Operator Theory and Partial Differential Equations (North Ryde, 1986), Proc. Centre Math. Anal. Austral. Nat. Univ. 14, Canberra, 1986, 210-231. 
11. [McQ1] A. McIntosh and T. Qian, Convolution singular integral operators on Lipschitz curves, in: Lecture Notes in Math. 1494, Springer, 1991, 142-162. Zbl0791.42012
12. [McQ2] A. McIntosh and T. Qian, Singular integrals along Lipschitz curves with holomorphic kernels, Approx. Theory Appl. 6 (1990), 40-57. Zbl0737.42017
13. [McQ3] A. McIntosh and T. Qian, Fourier multipliers on Lipschitz curves, Trans. Amer. Math. Soc. 333 (1992), 157-176. Zbl0766.42005
14. [Q1] T. Qian, Singular integrals on the m-torus and its Lipschitz perturbations, in: Clifford Algebras in Analysis and Related Topics, Stud. Adv. Math., CRC Press, Boca Raton, Fla., 1995, 94-108. 
15. [Q2] T. Qian, Transference from Lipschitz graphs to periodic Lipschitz graphs, in: Miniconference on Analysis and Applications (Brisbane, 1993), Proc. Centre Math. Appl. Austral. Nat. Univ. 33, Canberra, 1994, 189-194. 
16. [Q3] T. Qian, Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space, preprint. 
17. [Q4] T. Qian, A holomorphic extension result, Complex Variables Theory Appl. 32 (1996), 59-77. 
18. [Q5] T. Qian, Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space and generalizations to ${ℝ}^n$, in: Proc. Conf. on Clifford and Quaternionic Analysis and Numerical Methods, June 1996, to appear. 
19. [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501
20. [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971. 
21. [V] G. Verchota, Layer potentials and regularity for the Dirichlet problems for Laplace's equation in Lipschitz domains, J. Funct. Anal. 59 (1984), 572-611. Zbl0589.31005
22. [Z] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, London and New York, 1968. Zbl0157.38204