Publications of Alan M^{c}Intosh
Refereed Articles  Lectures and Surveys  Submitted or in Preparation  Proceedings Edited  Alan's Home Page
Refereed Articles
 with T. Hytönen and P. Portal, Holomorphic functional calculus of HodgeDirac operators in L^{p}, Journal of Evolution Equations, to appear, 25 pages. arXiv:0907.2274
 with Tuomas Hytönen, Stability in p of the H^{∞}calculus of first order systems in L^{p}, 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
 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
 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
 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
 with Pascal Auscher and Andreas Axelsson, Solvability of elliptic systems with square integrable boundary data, Arkiv för Matematik, published on line (DOI 10.1007/s1151200901082) (2009). arXiv:0809.4968
 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
 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
 with P. Auscher and E. Russ, Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds, Comptes Rendus Mathematiques 344 (2007), 103–108.
 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
 with Andreas Axelsson and Stephen Keith, Quadratic
estimates and functional calculi of perturbed Dirac operators,
Inventiones Mathematicae 163 (2006), 455–497. arXiv:math/0412321
 with Andreas Axelsson, Hodge decompositions on weakly
Lipschitz domains, Advances in Analysis and Geometry:
New Developments Using Clifford Algebras, Birkhauser (2004), 3–29.
 with Zengjian Lou, Hardy spaces of exact forms on
Lipschitz domains in R^{n},
Indiana Univ. Math. Journal 53 (2004), 583–611.
 with Zengjian Lou, Divergencefree Hardy space
on R^{n}_{+}, Science in China, Ser. A (in English)
47 (2004), 198–208.
 with Zengjian Lou, Divergencefree Hardy space
on R^{n}_{+}, Science in China, Ser. A (in Chinese)
33 (2003), 621–630
 with Zengjian Lou, Hardy spaces of exact forms on R^{N},
Transactions of the American Mathematical Society 357 (2005), 1469–1496.
 with P. Auscher, S. Hofmann
and Ph. Tchamitchian, The Kato square root problem for higher order
elliptic operators and systems on R^{n}, J. Evolution Equations 1 (2001),
361–385.
 with P. Auscher, S. Hofmann, M. Lacey
and Ph. Tchamitchian The solution of the Kato square root
problem for second order elliptic operators on R^{n}, Annals of Mathematics (2002) 156, 633–654.
 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.
 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.
 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.
 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.
 with X.T. Duong, The L^{p} 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.
 with Brian Jefferies and James PictonWarlow, The monogenic functional calculus,
Studia Math. 136 (1999), 99–119.
 with Brian Jefferies, The Weyl calculus and Clifford analysis,
Bulletin of the Australian Mathematical Society 57 (1998), 329–341.
 with Marius Mitrea,
Clifford algebras and Maxwell's equations in Lipschitz domains,
Mathematical Methods in the Applied Sciences 22 (1999), 1599–1620.
 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.
 with X.T. Duong, Singular integral operators with nonsmooth
kernels on irregular domains, Revista Matemática Iberoamericana 15 (1999), 233–265
 with Edwin Franks, Discrete quadratic estimates and
holomorphic functional calculi in Banach spaces,
Bulletin of the Australian Mathematical Society
58 (1998), 271–290.
 with Andrea Nahmod, Heat kernel estimates and
functional calculi of bΔ, Math. Scand. 87 (2000), 287–319.
 with David Albrecht and Edwin Franks,
Holomorphic functional calculi and sums
of commuting operators,
Bulletin of the Australian Mathematical Society
58 (1998), 291–305.
 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.
 with Pascal Auscher and Andrea Nahmod,
Holomorphic functional calculi of operators,
quadratic estimates and interpolation, Indiana
University Math. Journal 146 (1997), 375–403.
 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.
 with Pascal Auscher and Philippe Tchamitchian, Heat kernels of second order
complex elliptic operators and applications, Journal of Functional
Analysis 152 (1998), 22–73.
 with Pascal Auscher and Philippe Tchamitchian,
Noyau de la chaleur d'opérateurs elliptiques complexes, Math. Research
Letters 1 (1994), 35–43.
 with Chun Li, Z.J. Wu and Kewei Zhang, Compensated
compactness, paracommutators, and Hardy spaces, Journal of Functional
Analysis 150 (1997), 289–306.
 with X. T. Duong, Functional calculi of second order
elliptic operators with bounded measurable coefficients, Journal of Geometric
Analysis 6 (1996), 181–205.
 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
 with C. Li and T. Qian, Clifford algebras,
Fourier transforms, and singular convolution operators on Lipschitz surfaces,
Revista Matemática Iberoamericana 10 (1994), 665–721.
 with Tao Qian, Fourier multipliers on Lipschitz curves,
Transactions of the American Mathematical Society 333 (1992), 157–176.
 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.
 with C. Li and S. Semmes, Convolution singular integrals on Lipschitz surfaces, Journal of the American Mathematical Society 5 (1992), 455–481
 with Tao Qian, Singular integrals along Lipschitz curves with holomorphic
kernels, Approximation Theory and its Applications 6 (1990), 40–57.
 Clifford algebras and the higher dimensional Cauchy integral, Approximation Theory and Function Spaces 22 (1989), Banach Center Publications, 253–267.
 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.
 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.
 with A. Pryde and W. Ricker, Estimates for solutions of the
operator equation ∑A_{j}QB_{j} = U, Proc. of the 11th International
Conf. on Operator Theory, Bucharest 1986, Operator Theory: Advances and
Applications 28 (1988), Birkhäuser Verlag, Basel, 197–207.
 with A. Pryde and W. Ricker, Comparison of joint spectra for certain classes of commuting operators, Studia Math. 88 (1988), 23–36.
 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.
 with A. Pryde, A functional calculus for
several commuting operators, Indiana University Math. Journal 36 (1987), 421–439
 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.
 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.
 Square roots of elliptic operators,
Journal of Functional Analysis 61 (1985), 307–327.
 with Yves Meyer, Algèbres d'opérateurs définis par des intégrales singulières,
Comptes Rendus Acad. Sci., Paris, Sér. I, Math 301 (1985).
 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.
 with R. Bhatia and Ch. Davis, Perturbation of spectral
subspaces of normal operators, Linear Algebra and its Applications
52/53 (1983), 45–67.
 with R.R. Coifman and Y. Meyer, Estimations L^{2}
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.
 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.
 with R.R. Coifman and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur L^{2} pour les
courbes lipschitziennes, Annals of Mathematics 116 (1982), 361–387.
 On representing closed accretive
sesquilinear forms as (A^{½}u, A*^{½}v),
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.
 Second order properly elliptic boundary
value problems on irregular
plane domains, Journal of Differential Equations
34 (1979), 361–392.
 The Toeplitz–Hausdorff theorem and ellipticity conditions,
American Mathematical Monthly 85 (1978), 475–477.
 Functions and derivations of C*algebras, Journal of Functional Analysis 30 (1978), 264–275.
 On the comparability of A^{½} and A*^{½},
Proceedings of the American Mathematical Society 32 (1972), 430–434.
 Counterexample to a question on commutators, Proceedings of
the American Mathematical Society
29 (1971), 337–340.
 Hermitian bilinear forms which are not semibounded,
Bulletin of the American Mathematical Society 76 (1970), 732–737.
 Bilinear forms in Hilbert space, Journal of Mathematics and
Mechanics 19 (1970), 1027–1045.
 On the closed graph theorem, Proceedings of
the American Mathematical Society 20 (1969), 397–404.
 Representation of bilinear forms in Hilbert
space by linear operators,
Transactions of
the American Mathematical Society 31 (1968), 365–377.
