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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Wróbel, Błażej 2017. Joint Spectral Multipliers for Mixed Systems of Operators. Journal of Fourier Analysis and Applications, Vol. 23, Issue. 2, p. 245.
    Wróbel, Błażej 2012. Multivariate spectral multipliers for tensor product orthogonal expansions. Monatshefte für Mathematik, Vol. 168, Issue. 1, p. 125.
    Fraser, Andrea 2007. Singular integral operators of near-product-type on the Heisenberg group. Journal of Mathematical Analysis and Applications, Vol. 327, Issue. 2, p. 1225.
    Astengo, Francesca and Blasio, Bianca Di 2006. The Gelfand transform of homogeneous distributions on Heisenberg type groups. Journal of the Australian Mathematical Society, Vol. 81, Issue. 03, p. 297.
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Convolution kernels of (n + 1)-fold Marcinkiewicz multipliers on the Heisenberg group

  • A. J. Fraser (a1)
Abstract

We prove a characterisation, in terms of regularity and cancellation conditions, of the convolution kernels of Marcinkiewicz multiplier operators m (𝔏1,…,𝔏n, iT) on the Heisenberg group ℍn, where 𝔏1,…,𝔏n are the n partial sub-Laplacians. The necessity of these regularity and cancellation conditions was established by Fraser (2001); here, we prove their sufficiency.

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Copyright
COPYRIGHT: © Australian Mathematical Society 2001
References
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[1]Chang, S.Y. and Fefferman, R., ‘Some recent developments in Fourier analysis and H p theory on product domains’, Bull. Amer. Math. Soc. 12 (1985), 1–43.
[2]Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G., Higher transcendental functions, II (McGraw-Hill, New York, Toronto, London, 1953).
[3]Fraser, A.J., ‘An (n+1)–fold Marcinkiewicz multiplier theorem on the Heisenberg group’, Bull. Austral. Math. Soc. 63 (2001), 35–38.
[4]Geller, D., ‘Fourier analysis on the Heisenberg group’, Proc. Nat. Acad. Sci. U. S. A. 74 (1977), 1328–1331.
[5]Journé, J.L., ‘Calderón-Zygmund operators on product spaces’, Rev. Mat. Iberoamericana 1 (1985), 55–92.
[6]Müller, D., Ricci, F. and Stein, E.M., ‘Marcinkiewicz multipliers and two-parameter structures on Heisenberg groups, I’, Invent. Math. 119 (1995), 199–233.
[7]Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Mathematical Series 30 (Princeton Univ. Press, Princeton, N.J., 1970).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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