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On \(\mathcal M\)-harmonic space \({\mathcal B}^ s_ p\). (English) Zbl 0890.32001
The author proves that an \(M\)-harmonic function \(f\) in the unit ball in \(\mathbb{C}^n\) belongs to the Besov space \(B^s_p\) if and only if one of the following conditions holds: \[ \int_B |\tilde\nabla f(z) |^p (1 - |z |^2)^s dV(z) < \infty, \]
\[ \int_B |\nabla f(z) |^p (1 - |z |^2)^{s+p} dV(z) < \infty, \]
\[ \int_B |(1 - |z |^2)^{s+p} ( |Rf(z) |+ |\overline R f(z) |^p) dV(z) < \infty. \] This is then used to characterize functions in \(B^s_p\) depending on the size of \(s\) relative to \(-p\) and \(n\).
MSC:
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
46E15 Banach spaces of continuous, differentiable or analytic functions
32U05 Plurisubharmonic functions and generalizations
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