A Characterization of Some Classes of Harmonic Functions

In this paper we investigate harmonic Hardy-Orlicz and Bergman-Orlicz b _φ,α (B) spaces, using an identity of Hardy-Stein type. We also extend the notion of the Lusin property by introducing (φ, α)-Lusin property with respect to a Stoltz domain. The main result in the paper is as follows: Let be a nonnegative increasing convex function twice differentiable on (0, ∞), and u a harmonic function on the unit ball B in . Then the following statements are equivalent:

(a)	.
(b)	.
(c)	u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for any .
(d)	u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for some .