Characterisation of the L p Range of the Gen- eralised Poisson Transform\n of the hyperbolic space B(H n )

2017/12/13 by Imane Ghanimi, Ghanimi, Imane
Mathematics · Physics and Astronomy · #Mathematics and Applications #Algebraic and Geometric Analysis #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1712.04634

Abstract

The aim of this paper is to give the characterisation of the L p Range (p\n\≥ 2) of the Generalised Poisson Transform of the Hyperbolic space B(H n),\n(n \≥ 2), over the classical field of the quaternions H. Namely, if f is an\nhyperfunction in the boundary of B(H n), then we show that f is in L p\n(\∂B(H n)) if and only if it's generalised poisson transform satisfy an\nHardy type growth condition. An explicit expression of the generalized\nspherical functions is given. Mathematics Subject Classification (2010).\nPrimary 22E46; Secondary 33Cxx.\n

Related

• A characterization of the L²-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces
• Characterization of the Lp-range of the Poisson transform on the\n Octonionic Hyperbolic Plane
• A characterization of the L²-range of the generalized spectral projections related to the Hodge-de Rham Laplacian
• On Poisson transforms of differential forms on real hyperbolic spaces
• Poisson transforms, the BGG complex, and discrete series representations of SU(n+1,1)