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Spherical means and CR functions on the Heisenberg group

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Abstract

The injectivity of the spherical mean value operator on the Heisenberg group is studied. Whenf ∈L P (Hn), 1 ≤p < ∞ it is proved that the spherical mean value operator is injective. When 1 ≤p ≤ 2,f(z, ·) ∈L P (ℝ) the same is proved under much weaker conditions in the z-variable. Some extensions of recent results of Agranovskyet al. regardingCR functions on the Heisenberg group are also obtained.

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Authors and Affiliations

  1. White Hall Cornell University, 14859, Ithaca, NY, USA

    S. Thangavelu

  2. T. I. F. R. Centre, I.I. Sc. Campus, 560012, Bangalore, India

    S. Thangavelu

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  1. S. Thangavelu
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Thangavelu, S. Spherical means and CR functions on the Heisenberg group. J. Anal. Math. 63, 255–286 (1994). https://doi.org/10.1007/BF03008426

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  • DOI: https://doi.org/10.1007/BF03008426

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