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\(\mathcal M\)-harmonic Besov \(p\)-spaces and Hankel operators in the Bergman space on the ball in \(\mathbb{C}^ n\). (English) Zbl 0816.31004
The authors establish a reproducing formula for \({\mathcal M}\)-harmonic functions in \(h^ p (B)\), the space of all \({\mathcal M}\)-harmonic functions \(f\) on the unit ball \(B = B^ n \subseteq \mathbb{C}^ n\) that satisfy a growth condition. Extending the definition of Besov \(p\)-spaces to \({\mathcal M}\)-harmonic functions on \(B\), they obtain several characterizations of \({\mathcal M} B_ p (B)\). Various equivalent conditions are also obtained for the Hankel operators \(H_ f\) and \(H_{\overline f}\) to be bounded, compact or to lie in the Schatten-von-Neumann class.
Some corrections are given in the Erratum (Zbl 0816.31005) stated below.
Reviewer: P.C.Sinha (Patna)

MSC:
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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