A Characterization of Some Classes of Harmonic Functions |
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Authors: | Stevo Stević |
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Institution: | (1) Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, 11000 Beograd, Serbia |
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Abstract: | 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:
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(b) |
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u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for any .
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(d) |
u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for some .
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 31B05 |
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