Publications of Michael Cowling

Most of the later papers are available in preprint form, through the UNSW institutional repository UNSWorks. In addition, publishers such as the American and Australian Mathematical Societies make all the articles that they publish freely available five years after publication.

Return to Michael Cowling's home page.

  1. Extension of multipliers by periodicity, Bull. Austral. Math. Soc. 6 (1972), 263-285.
  2. Extension of Fourier Lp-Lq multipliers, Trans. Amer. Math. Soc. 213 (1975), 1-33.
  3. Functions which are restrictions of Lp-multipliers, Trans. Amer. Math. Soc. 213 (1975), 35-51.
  4. Inclusions and noninclusions of spaces of convolution operators, with J.J.F. Fournier, Trans. Amer. Math. Soc. 221 (1976), 59-95.
  5. The Kunze-Stein phenomenon, Rend. Sem. Mat. Fis. Milano 46 (1976), 35-41.
  6. The Kunze-Stein phenomenon, Bull. Amer. Math. Soc. 83 (1977), 293-295.
  7. La synthèse des convoluteurs de Lp de certains groupes pas moyennables, Boll. Un. Mat. Ital. 14-A (1977), 551-555. Erratum, Boll. Un. Mat. Ital. 1 (1982), 317.
  8. The Kunze-Stein phenomenon, Ann. of Math. 107 (1978), 209-234.
  9. The Plancherel formula for a group not of type I, Boll. Un. Mat. Ital. 15-A (1978), 616-623.
  10. Some applications of Grothendieck's theory of topological tensor products in harmonic analysis, Math. Ann. 232 (1978), 273-285.
  11. An application of Littlewood-Paley theory in harmonic analysis, Math. Ann. 241 (1979), 83-96.
  12. The Fourier-Stieltjes algebra of a semisimple group, Colloq. Math. 41 (1979), 89-94.
  13. Restriction of certain function spaces to closed subgroups of locally compact groups, with P. Rodway, Pacific J. Math. 80 (1979), 91-104.
  14. Sur les coefficients des représentations unitaires des groupes de Lie simples, Lecture Notes in Math. 739 (1979), 132-178.
  15. Fractional integration on nilpotent groups and representations of semi-simple groups, Proc. Symp. Pure Math. 35, Part 2, (1979), 395-402.
  16. On maximal functions, with G. Mauceri, Rend. Sem. Mat. Fis. Milano 49 (1979), 79-87.
  17. On Littlewood-Paley-Stein theory, Suppl. Rend. Circ. Mat. Palermo 1 (1981), 21-55.
  18. A remark on twisted convolution, Suppl. Rend. Circ. Mat. Palermo 1 (1981), 203-209.
  19. Examples of twisted convolution operators, with A.M. Mantero, Lecture Notes in Math. 908 (1982), 210-216.
  20. Pointwise estimates for some kernels on compact Lie groups, with A.M. Mantero and F. Ricci, Rend. Circ. Mat. Palermo (II) XXXI (1982), 145-158.
  21. Unitary and uniformly bounded representations of some simple Lie groups, in: Harmonic Analysis and Group Representations, C.I.M.E. II ciclo 1980, 49-128. Liguori, Napoli, 1982.
  22. Harmonic analysis on semigroups, Ann. of Math. 117 (1983), 267-283.
  23. Pointwise behaviour of solutions to Schrödinger equations, Lecture Notes in Math. 992 (1983), 83-90.
  24. Generalisation of Heisenberg's inequality, with J.F. Price, Lecture Notes in Math. 992 (1983), 443-449.
  25. Harmonic analysis on some nilpotent groups (with applications to the representation theory of some semisimple Lie groups), in: Topics in Modern Harmonic Analysis, Vol. I, 81-123. Istituto Nazionale di Alta Matematica, Roma, 1983.
  26. Bandwidth versus time concentration: the Heisenberg-Pauli-Weyl inequality, with J.F. Price, SIAM J. Math. Anal. 15 (1984), 151-165.
  27. On representations in Banach spaces, with G. Fendler, Math. Ann. 266 (1984), 307-315.
  28. Harmonic analysis on Heisenberg type groups from a geometric viewpoint, with A. Korányi, Lecture Notes in Math. 1077 (1984), 60-100.
  29. Inequalities for some maximal functions I, with G. Mauceri, Trans. Amer. Math. Soc. 287 (1985), 431-455.
  30. Square functions in Banach spaces, Proc. Centre Math. Anal. 9 (1985), 177-184.
  31. On the Paley-Wiener theorem, Invent. Math. 83 (1986), 403-404.
  32. Inequalities for some maximal functions II, with G. Mauceri, Trans. Amer. Math. Soc. 296 (1986), 341-365.
  33. Semigruppi negli spazi di Banach, Rend. Sem. Mat. Fis. Milano 53 (1986), 27-33.
  34. On isomorphisms of algebras of operators, Proc. Centre Math. Anal. 14 (1986), 11-20.
  35. Fourier transforms of surface carried measures, with G. Mauceri, Proc. Centre Math. Anal. 14 (1986), 142-147.
  36. Oscillatory integrals and Fourier transforms of surface carried measures, with G. Mauceri, Trans. Amer. Math. Soc. 304 (1987), 53-68.
  37. Oscillatory integrals, with S. Disney, Proc. Centre Math. Anal. 15 (1987), 45-54.
  38. Rigidity, von Neumann algebras and semisimple groups, Proc. Centre Math. Anal. 16 (1988), 51-57.
  39. Almost L2 matrix coefficients, with U. Haagerup and R. Howe, J. reine angew. Math. 387 (1988), 97-100.
  40. On the characters of unitary representations, J. Austral. Math. Soc. Ser. A 45 (1988), 62-65.
  41. A qualitative uncertainty principle for semisimple Lie groups, with J.F. Price and A. Sitaram, J. Austral. Math. Soc. Ser. A 45 (1988), 127-132.
  42. Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one, with U. Haagerup, Invent. Math. 96 (1989), 507-549.
  43. Actions of lattices in Sp(1,n), with R.J. Zimmer, Ergod. Th. Dynam. Sys. 9 (1989), 221-237.
  44. Variants of Littlewood-Paley theory, with G. Fendler and J.J.F. Fournier, Math. Ann. 285 (1989), 333-342.
  45. On a maximal function on compact Lie groups, with C. Meaney, Trans. Amer. Math. Soc. 315 (1989), 811-822.
  46. A note on martingales with respect to complex measures, with G.I. Gaudry and T. Qian, Proc. Centre Math. Anal. 24 (1990), 10-27.
  47. Surface measures-Maximal functions and Fourier transforms, with G. Mauceri, Proc. Centre Math. Anal. 24 (1990), 28-37.
  48. Damping oscillatory integrals, with S.A.R. Disney, G. Mauceri, and D. Müller, Invent. Math. 101 (1990), 237-260.
  49. Weak type (1,1) estimates for heat kernel maximal functions on Lie groups, with G. Gaudry, S. Giulini, and G. Mauceri, Trans. Amer. Math. Soc. 323 (1991), 637-649.
  50. H-type groups and Iwasawa decompositions, with A.H. Dooley, A. Korányi and F. Ricci, Adv. in Math. 87 (1991), 1-41.
  51. Rigidity for lattices in semisimple Lie groups: von Neumann algebras and ergodic actions, Rend. Sem. Mat. Univ. Pol. Torino 47 (1989), 1-37.
  52. The irreducibility of restrictions of unitary representations to lattices, with T. Steger, J. reine angew. Math. 420 (1991), 85-98.
  53. Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces I, with S. Giulini and S. Meda, Duke Math. J. 72 (1993), 109-150.
  54. Harmonic analysis and ultracontractivity, with S. Meda, Trans. Amer. Math. Soc. 340 (1993), 733-752.
  55. Simplicity of the reduced C*-algebra of PSL(n,Z), with M. Bekka and P. de la Harpe, Intern. Math. Res. Notices 7 (1994), 285-291.
  56. Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth, with S. Giulini, A. Hulanicki, and G. Mauceri, Studia Math. 111 (1994), 103-121.
  57. Some groups whose reduced C*-algebra is simple, with M. Bekka and P. de la Harpe, Inst. Hautes Etudes Sci. Publ. Math. 80 (1994), 117-134.
  58. Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces II, with S. Giulini and S. Meda, J. Lie Theory 5 (1995), 1-14.
  59. Banach space operators with a bounded H functional calculus, with I. Doust, A. McIntosh, and A. Yagi, J. Austral. Math. Soc. Ser. A 60 (1996), 51-89.
  60. Herz' ``principe de majoration'' and the Kunze-Stein phenomenon, CMS Conf. Proc. 21 (1997), 73-88.
  61. Random subgroups of Lie groups, with B. Dorofaeff, Rend. Sem. Mat. Fis. Milano 67 (1997), 95-101.
  62. The predual of the space of convolutors on a locally compact group, Bull. Austral. Math. Soc. 57 (1998), 409-414.
  63. An overview of harmonic analysis on the group of isometries of a homogeneous tree, with S. Meda and A.G. Setti, Exposition. Math. 16 (1998), 385-423.
  64. An approach to symmetric spaces of rank one via groups of Heisenberg type, with A.H. Dooley, A. Korányi, and F. Ricci, J. Geom. Anal. 8 (1998), 199-237.
  65. The range of the Helgason-Fourier transformation on homogeneous trees, with A.G. Setti, Bull. Austral. Math. Soc. 59 (1999), 237-246.
  66. Invariant operators on functions spaces on homogeneous trees, with S. Meda and A.G. Setti, Colloq. Math. 80 (1999), 53-61.
  67. Riesz potentials and amalgams, with S. Meda and R. Pasquale, Annales Inst. Fourier (Grenoble) 49 (1999), 1345-1367.
  68. A class of singular integrals on the n-complex unit sphere, with T. Qian, Science in China (Ser. A) 42 (1999), 1233-1245.
  69. Hardy's uncertainty principle on semisimple groups, with A. Sitaram and M. Sundari, Pacific J. Math. 192 (2000), 293-296.
  70. Estimates for functions of the Laplace operator on homogeneous trees, with S. Meda and A.G. Setti, Trans. Amer. Math. Soc. 352 (2000), 4271-4293.
  71. Mappings which preserve families of curves, in: Proceedings of the X Indonesian National Conference on Mathematics, Sriwulan Adji and Janson Naiborhu (eds), Majalah Ilmiah Himpunan Mathematika Indonesia 6 (No. 5) (2000), 67-72.
  72. Hardy's uncertainty principle on certain Lie groups, with F. Astengo, B. Di Blasio, and M. Sundari, J. London Math. Soc. (2) 62 (2000), 461-472.
  73. Characterization of Lie groups with the Haagerup property, with P.-A. Cherix and A. Valette, in: Groups with the Haagerup property, pages 43-64 in: Progress in Mathematics, Vol. 197. Birkhaüser, Basel, 2001.
  74. The radial Haagerup property, in: Groups with the Haagerup property, pages 65-87 in: Progress in Mathematics, Vol. 197. Birkhaüser, Basel, 2001.
  75. A spectral multiplier theorem for a sublaplacian on SU(2), with A. Sikora, Math. Zeits. 238 (2001), 1-36. The original publication is available in LINK at http://link.springer.de.
  76. Lp-Lq estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces III, with S. Giulini and S. Meda, Annales Inst. Fourier (Grenoble) 51 (2001), 1047-1069.
  77. Light on Littlewood-Paley theory, with T. Tao, Math. Ann. 321 (2001), 885-888. The original publication is available in LINK at http://link.springer.de.
  78. Uniform estimates for spherical functions on complex semisimple Lie groups, with A. Nevo, Geom. Funct. Anal. 11 (2001), 900-932.
  79. Analysis on the sphere, Jurnal Matematika atau pembelajarannya VIII (2002), 179-183.
  80. Weighted estimates for fractional maximal functions related to spherical means, with J. Garcia Cuerva and H. Gunawan, Bull. Austral. Math. Soc. 66 (2002), 75-90.
  81. Oscillatory multipliers related to the wave equation on noncompact symmetric spaces, with S. Giulini and S. Meda, J. London Math. Soc. 66 (2002), 691-709.
  82. Some unitary representations of G(K) for a simple algebraic group over a field K, with M.E.B. Bekka, Math. Z. 241 (2002), 731-741. The original publication is available in LINK at http://link.springer.de.
  83. Contact and conformal maps on Iwasawa N groups, with F. De Mari, A. Korányi and H.M. Reimann, Rend. Mat. Acc. Lincei 13 (2002), 219-232.
  84. Quasiconformal mappings on Carnot groups: three examples, with H.M. Reimann, Contemp. Math. 320 (2003), 111-118.
  85. Filter products of C0 semigroups and ultraproduct representations for Lie groups, with P.-A. Cherix and B. Straub, J. Funct. Anal. 208 (2004), 31-63.
  86. The Cayley transform and uniformly bounded representations, with F. Astengo and B. Di Blasio, J. Funct. Anal. 213 (2004), 241-269.
  87. Contact and conformal maps in parabolic geometry. I , with F. De Mari, A. Korányi and H.M. Reimann, Geom. Dedic. 111 (2005), 65-86.
  88. A family of singular oscillatory integral operators and failure of weak amenability, with B.A. Dorofaeff, A. Seeger and J. Wright, Duke Math. J. 127 (2005), 429-485.
  89. Measure theory and automorphic representations, Bull. Kerala Math. Assoc. 3 (Special issue) (2006), 139-153.
  90. Estimates for kernels of intertwining operators on SL(n,R), with S. Meda, J. Austral. Math. Soc. 81 (2006), 105-120.
  91. Conformality and Q-harmonicity in Carnot groups, with L. Capogna, Duke Math J. 135 (2006), 455-479.
  92. An uncertainty principle for operators, pages 43-46 in: Wavelet Analysis and Applications, edited by T. Qian, M.I. Vai, Y. Xu. Applied and Numerical Harmonic Analysis Series. Birkhaüser, Basel, 2007.
  93. The Heisenberg group, SL(3,R) and rigidity, with A. Čap, F. De Mari, M. Eastwood, and R. McCallum, pages 41-52 in: Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory , edited by Jian-Shu Li, Eng-Chye Tan, Nolan Wallach and Chen-Bo Zhu. World Scientific, Singapore, 2007.
  94. Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa), pages 1-50 in: Representation Theory and Complex Analysis, E. Casadio Tarabusi, A. D'Agnolo, and M. Picardello, eds, Lectures given at the C.I.M.E. Summer School in Venice, Italy, 2004. Lecture Notes in Math, Vol. 1931. Springer, New York-Heidelberg, 2008.
  95. Vector-valued distributions and Hardy's uncertainty principle for operators, with B. Demange and M. Sundari, Rev. Mat. Iberoamericana, 26 (2010), 133-146.
  96. A weak type (1,1) estimate for a maximal operator on a group of isometries of a homogeneous tree, with S. Meda and A. G. Setti, Colloq. Math. 118 (2010), 223-232.
  97. Spectral multipliers for the Kohn sublaplacian on the sphere in Cn, with O. Klima and A. Sikora, Trans. Amer. Math. Soc. 363 (2011), 611-631.
  98. Calculus on nilpotent Lie groups, pages 285-295 in: Geometry, Rigidity and Group Actions, B. Farb and D. Fisher eds, University of Chicago Press, Chicago, USA, 2011.
  99. Pointwise convergence and semigroups acting on vector-valued functions, with M. Leinert, Bull. Aust. Math. Soc. 84 (2011), 44-48.
  100. The Hardy uncertainty principle revisited, with L. Escauriaza, C.E. Kenig, G. Ponce, and L. Vega, Indiana U. Math. J. 59 (2010), 2007-2025 (published 2012).
  101. Isomorphisms of the Figà-Talamanca-Herz algebras Ap(G) for connected Lie groups G, pages 1-18 in: Colloquium De Giorgi 2009, U. Zannier ed. Edizione della Normale, Scuola Normale Superiore, Pisa, Italy, 2012.
  102. Sub-Finsler geometry and finite propagation speed, with A. Martini, pages 147-205 in: Trends in Harmonic Analysis, edited by M. A. Picardello. Springer INdAM Series, Vol. 3. Springer, Milan-Heidelberg-New York, 2013.
  103. Conformal mappings on Carnot groups, with A. Ottazzi, Ann. Acad. Sci. Fenn. Math. 40 (2015), 1-11.
  104. Hardy and uncertainty inequalities on stratified Lie groups, with P. Ciatti and F. Ricci, Adv. in Math. 277 (2015), 365-387.
  105. Global contact and quasiconformal mappings of Carnot groups, with A. Ottazzi, Conform. Geom. Dyn. 19 (2015), 221-239.
  106. Operator Lipschitz estimates in the unitary setting, with P. J. Ayre and F. A. Sukochev, Proc. Amer. Math. Soc. 144 (2016), 1053-1057.
  107. Structure of stratified groups I. Product decompositions, with A. Ottazzi, J. Lie Theory 27 (2017), 177-183. Available online.
  108. Behaviour of the Brascamp-Lieb constant, with J. Bennett, N. Bez and T. Flock, Bull. London Math. Soc. 49 (2017), 512-518. Available online.
  109. Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn, with V. Casarino, A. Martini and A. Sikora, J. Geom. Anal. 27 (2017), 3302-3338. Available online.
  110. Uniformly bounded representations and completely bounded multipliers of SL(2,R), with F. Astengo and B. Di Blasio, Adv. Operator Theory 3 (2018), 247-270. Available online.
  111. The root-space-preserving derivations of the nilpotent Iwasawa subalgebra of a real simple Lie algebra, with P. Ciatti, Annali di Matematica Pura Appl. 197 (2018), 233-259. Available online.
  112. The Levi decomposition of a graded Lie algebra, with P. Ciatti, Riv. Mat. Univ. Parma 9 (2018), 373-378. Available online.
  113. Uniformly bounded representations of SL(2,R), with F. Astengo and B. Di Blasio, J. Funct. Anal. 276 (2019), 127-147. Available online.
  114. The Hausdorff-Young inequality on Lie groups, with A. Martini, D. Müller, and J. Parcet, Math. Ann. 375 (2019), 93-131. Available online.
  115. Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres, with J. Ahrens, A. Martini, and D. Müller, Math. Zeit. 294 (2020), 1659-1686. Available online.
  116. Conformal and CR mappings on Carnot groups, with J. Li, A. Ottazzi and Q. Wu, Proc. Amer. Math. Soc. Ser. B 7 (2020), 67-81. Available online.
  117. On the nonlinear Brascamp-Lieb inequality, with J. Bennett, N. Bez, S. Buschenhenke and T. Flock, Duke Math. J. 169 (2020), 3291--3338. Available online.
Accepted for publication.
  • Estimates for matrix coefficients of representations, with T. Bruno, F. Nicola and A. Tabacco. To appear in Amer. J. Math.
  • Marcinkiewicz multipliers associated with the Kohn Laplacian on the Shilov boundary of the product domain in C2n, with Peng Chen, Guorong Hu, and Ji Li, To appear in Math. Zeits.
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