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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
##### Keywords:
$$M$$-harmonic function; Besov spaces; Bergman space
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