Publications of Alan McIntosh

Refereed Articles | Lectures and Surveys | Submitted or in Preparation | Proceedings Edited | Alan's Home Page

Refereed Articles

  1. with T. Hytönen and P. Portal, Holomorphic functional calculus of Hodge-Dirac operators in Lp, Journal of Evolution Equations, to appear, 25 pages. arXiv:0907.2274
  2. with Tuomas Hytönen, Stability in p of the H∞-calculus of first order systems in Lp, AMSI–ANU Workshop on Spectral Theory and Harmonic Analysis 2009, Proceedings of the Centre for Mathematics and its Applications 44 (2010), 167–181. arXiv:1003.5456
  3. with S. Hofmann and S. Mayboroda, Hardy spaces, Riesz transforms and functional calculus on Sobolev spaces for second order elliptic operators, Les Annales Scientifiques de l'Ecole Normale Supérieure, to appear, 77 pages. arXiv:1002.0792
  4. with Pascal Auscher and Andreas Axelsson, On a quadratic estimate related to the Kato conjecture and boundary value problems, Contemporary Mathematics, AMS 505 (2010), 105–129. arXiv:0810.3071
  5. with Martin Costabel, On Bogovskii and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains, Mathematische Zeitschrift 265 (2010), 297–320. arXiv:0808.2614
  6. with Pascal Auscher and Andreas Axelsson, Solvability of elliptic systems with square integrable boundary data, Arkiv för Matematik, published on line (DOI 10.1007/s11512-009-0108-2) (2009). arXiv:0809.4968
  7. with T Hytönen and P. Portal, Kato's square root problem in Banach spaces, Journal of Functional Analysis 254 (2008), 675–726. arXiv:math/0703012
  8. with P. Auscher and E. Russ, Hardy spaces of differential forms on Riemannian manifolds, Journal of Geometric Analysis 18 (2008), 192–248. arXiv:math/0611334
  9. with P. Auscher and E. Russ, Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds, Comptes Rendus Mathematiques 344 (2007), 103–108.
  10. with Andreas Axelsson and Stephen Keith, The Kato square root problem for mixed boundary value problems, Journal of the London Mathematical Society (2) 74 (2006), 113–130. arXiv:math/0412324
  11. with Andreas Axelsson and Stephen Keith, Quadratic estimates and functional calculi of perturbed Dirac operators, Inventiones Mathematicae 163 (2006), 455–497. arXiv:math/0412321
  12. with Andreas Axelsson, Hodge decompositions on weakly Lipschitz domains, Advances in Analysis and Geometry: New Developments Using Clifford Algebras, Birkhauser (2004), 3–29.
  13. with Zengjian Lou, Hardy spaces of exact forms on Lipschitz domains in Rn, Indiana Univ. Math. Journal 53 (2004), 583–611.
  14. with Zengjian Lou, Divergence-free Hardy space on Rn+, Science in China, Ser. A (in English) 47 (2004), 198–208.
  15. with Zengjian Lou, Divergence-free Hardy space on Rn+, Science in China, Ser. A (in Chinese) 33 (2003), 621–630
  16. with Zengjian Lou, Hardy spaces of exact forms on RN, Transactions of the American Mathematical Society 357 (2005), 1469–1496.
  17. with P. Auscher, S. Hofmann and Ph. Tchamitchian, The Kato square root problem for higher order elliptic operators and systems on Rn, J. Evolution Equations 1 (2001), 361–385.
  18. with P. Auscher, S. Hofmann, M. Lacey and Ph. Tchamitchian The solution of the Kato square root problem for second order elliptic operators on Rn, Annals of Mathematics (2002) 156, 633–654.
  19. with P. Auscher, S. Hofmann, M. Lacey, J. Lewis and Ph. Tchamitchian The solution of Kato's conjectures, Comptes Rendus Acad. Sci., Paris, Sér. I, Math 332 (2001), 601–606.
  20. with A. Axelsson, R. Grognard and J. Hogan Harmonic analysis of Dirac operators on Lipschitz domains, Proceedings of the Conference on Clifford Analysis and its Applications, Prague 2000, Kluwer (2001), 231–246.
  21. with Steve Hofmann and Michael Lacey, The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds, Annals of Mathematics 156 (2002), 623–631.
  22. with Steve Hofmann, The solution of the Kato problem in two dimensions, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain 2000, Publicacions Matemàtiques, Univ. Autònoma de Barcelona (2002), 143–160.
  23. with X.T. Duong, The Lp boundedness of Riesz transforms associated with divergence form operators, Workshop on Analysis and Applications, Brisbane, 1997, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra 37 (1999), 15–25.
  24. with Brian Jefferies and James Picton-Warlow, The monogenic functional calculus, Studia Math. 136 (1999), 99–119.
  25. with Brian Jefferies, The Weyl calculus and Clifford analysis, Bulletin of the Australian Mathematical Society 57 (1998), 329–341.
  26. with Marius Mitrea, Clifford algebras and Maxwell's equations in Lipschitz domains, Mathematical Methods in the Applied Sciences 22 (1999), 1599–1620.
  27. with Jeff Hogan, Chun Li and Kewei Zhang, Global higher integrability of Jacobians on bounded domains, Annales de l'Institut Henri Poincaré 17 (2000), 193–217.
  28. with X.T. Duong, Singular integral operators with non-smooth kernels on irregular domains, Revista Matemática Iberoamericana 15 (1999), 233–265
  29. with Edwin Franks, Discrete quadratic estimates and holomorphic functional calculi in Banach spaces, Bulletin of the Australian Mathematical Society 58 (1998), 271–290.
  30. with Andrea Nahmod, Heat kernel estimates and functional calculi of -bΔ, Math. Scand. 87 (2000), 287–319.
  31. with David Albrecht and Edwin Franks, Holomorphic functional calculi and sums of commuting operators, Bulletin of the Australian Mathematical Society 58 (1998), 291–305.
  32. with Pascal Auscher and Andrea Nahmod, The square root problem of Kato in one dimension, and first order elliptic systems, Indiana University Math. Journal 146 (1997), 659–695.
  33. with Pascal Auscher and Andrea Nahmod, Holomorphic functional calculi of operators, quadratic estimates and interpolation, Indiana University Math. Journal 146 (1997), 375–403.
  34. with Chun Li, Clifford algebras and H&infin functional calculi of commuting operators, Chapter 6 in Clifford Algebras in Analysis and Related Topics, edited by John Ryan, CRC Press (1996), 89–101.
  35. with Pascal Auscher and Philippe Tchamitchian, Heat kernels of second order complex elliptic operators and applications, Journal of Functional Analysis 152 (1998), 22–73.
  36. with Pascal Auscher and Philippe Tchamitchian, Noyau de la chaleur d'opérateurs elliptiques complexes, Math. Research Letters 1 (1994), 35–43.
  37. with Chun Li, Z.J. Wu and Kewei Zhang, Compensated compactness, paracommutators, and Hardy spaces, Journal of Functional Analysis 150 (1997), 289–306.
  38. with X. T. Duong, Functional calculi of second order elliptic operators with bounded measurable coefficients, Journal of Geometric Analysis 6 (1996), 181–205.
  39. with M. Cowling, I. Doust and A. Yagi, Banach space operators with a bounded H∞ functional calculus, Journal of the Australian Math. Society (Ser. A) 60 (1996), 51–89
  40. with C. Li and T. Qian, Clifford algebras, Fourier transforms, and singular convolution operators on Lipschitz surfaces, Revista Matemática Iberoamericana 10 (1994), 665–721.
  41. with Tao Qian, Fourier multipliers on Lipschitz curves, Transactions of the American Mathematical Society 333 (1992), 157–176.
  42. with T. Qian, Convolution singular integral operators on Lipschitz curves, Proceedings of the Special Year on Harmonic Analysis at Nankai Institute of Mathematics, Tianjin, China, Lecture Notes in Mathematics 1494 (1991), Springer–Verlag, 142–162.
  43. with C. Li and S. Semmes, Convolution singular integrals on Lipschitz surfaces, Journal of the American Mathematical Society 5 (1992), 455–481
  44. with Tao Qian, Singular integrals along Lipschitz curves with holomorphic kernels, Approximation Theory and its Applications 6 (1990), 40–57.
  45. Clifford algebras and the higher dimensional Cauchy integral, Approximation Theory and Function Spaces 22 (1989), Banach Center Publications, 253–267.
  46. Operators of type ω without a bounded H∞ functional calculus, Miniconference on Operators in Analysis, 1989, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra 24 (1989), 159–172.
  47. with Alan Pryde and Werner Ricker, Systems of operator equations and perturbation of spectral subspaces of commuting operators, Michigan Math. Journal 35 (1988), 43–65.
  48. with A. Pryde and W. Ricker, Estimates for solutions of the operator equation ∑AjQBj = U, Proc. of the 11th International Conf. on Operator Theory, Bucharest 1986, Operator Theory: Advances and Applications 28 (1988), Birkhäuser Verlag, Basel, 197–207.
  49. with A. Pryde and W. Ricker, Comparison of joint spectra for certain classes of commuting operators, Studia Math. 88 (1988), 23–36.
  50. with T. Qian, Fourier theory on Lipschitz curves, Miniconference on Harmonic Analysis, 1987, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra 15 (1987), 157–166.
  51. with A. Pryde, A functional calculus for several commuting operators, Indiana University Math. Journal 36 (1987), 421–439
  52. Operators which have an H∞ functional calculus, Miniconference on Operator Theory and Partial Differential Equations, 1986, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra 14 (1986), 210–231.
  53. with A. Pryde, The solution of systems of operator equations using Clifford algebras, Miniconference on Linear Analysis and Function Spaces 1984, Proceeings of the Centre for Mathematical Analysis, ANU, Canberra 9, (1985), 212–222.
  54. Square roots of elliptic operators, Journal of Functional Analysis 61 (1985), 307–327.
  55. with Yves Meyer, Algèbres d'opérateurs définis par des intégrales singulières, Comptes Rendus Acad. Sci., Paris, Sér. I, Math 301 (1985).
  56. Square roots of operators and applications to hyperbolic p.d.e.'s, Miniconference on Operator Theory and Partial Differential Equations 1983, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra 5 (1984), 124–136.
  57. with R. Bhatia and Ch. Davis, Perturbation of spectral subspaces of normal operators, Linear Algebra and its Applications 52/53 (1983), 45–67.
  58. with R.R. Coifman and Y. Meyer, Estimations L2 pour les noyaux singuliers, Conference on Harmonic Analysis in Honor of Antoni Zygmund, edited by Beckner, Calderóon, Fefferman and Jones, Wadsworth Mathematical Series (1983), 287–294.
  59. with R.R. Coifman and Y. Meyer, The Hilbert transform on Lipschitz curves, Miniconference on Partial Differential Equations, 1981, Proceedings of the Centre for Mathematical Analysis, ANU, Canberra 1 (1982), 26–69.
  60. with R.R. Coifman and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur L2 pour les courbes lipschitziennes, Annals of Mathematics 116 (1982), 361–387.
  61. On representing closed accretive sesquilinear forms as (A½u, A*½v), Collège de France Seminar, Volume III, edited by H. Brezis and J.L. Lions, Pitman Advanced Publishing Program, Research Notes in Math.70 (1982), 252–267.
  62. Second order properly elliptic boundary value problems on irregular plane domains, Journal of Differential Equations 34 (1979), 361–392.
  63. The Toeplitz–Hausdorff theorem and ellipticity conditions, American Mathematical Monthly 85 (1978), 475–477.
  64. Functions and derivations of C*-algebras, Journal of Functional Analysis 30 (1978), 264–275.
  65. On the comparability of A½ and A*½, Proceedings of the American Mathematical Society 32 (1972), 430–434.
  66. Counterexample to a question on commutators, Proceedings of the American Mathematical Society 29 (1971), 337–340.
  67. Hermitian bilinear forms which are not semi-bounded, Bulletin of the American Mathematical Society 76 (1970), 732–737.
  68. Bilinear forms in Hilbert space, Journal of Mathematics and Mechanics 19 (1970), 1027–1045.
  69. On the closed graph theorem, Proceedings of the American Mathematical Society 20 (1969), 397–404.
  70. Representation of bilinear forms in Hilbert space by linear operators, Transactions of the American Mathematical Society 31 (1968), 365–377.