Hua operators and Poisson transform for bounded symmetric domains
Journal article, 2006

Let Ω be a bounded symmetric domain of non-tube type in C n with rank r and S its Shilov boundary. We consider the Poisson transform P s f ( z ) for a hyperfunction f on S defined by the Poisson kernel P s ( z, u ) = ( h ( z, z ) n / r / | h ( z, u ) n / r | 2 ) s , ( z, u ) × Ω × S, s ∈ C. For all s satisfying certain non-integral condition we find a necessary and sufficient condition for the functions in the image of the Poisson transform in terms of Hua operators. When Ω is the type I matrix domain in M n, m ( C ) ( n {less-than or slanted equal to} m), we prove that an eigenvalue equation for the second order M n, n -valued Hua operator characterizes the image. © 2006 Elsevier Inc. All rights reserved.

tube type




invariant differential-operators


K. Koufany

Henri Poincaré University

Genkai Zhang

Chalmers, Mathematical Sciences

University of Gothenburg

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 236 2 546-580

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