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1980
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Howard L. Jackson, « On the boundary behaviour of BLD functions and some applications », Bulletins de l'Académie Royale de Belgique, ID : 10.3406/barb.1980.58628
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Our results indicate that if u is a BLD potential on the unit disk Ω then u has a minimal fine limit in the sense of J. Lelong-Ferrand ([17]) and L. Naïm ([18]) everywhere on the unit circle. If h ∈ HD(Ω) where HD(Ω) constitutes the space of Dirichlet finite (or BLD) harmonic functions then we have also proved that the minimal fine cluster set is always contained in the radial cluster set at every point on the unit circle. For any BLD function on Ω it is therefore true that its minimal fine cluster set at any point of the unit circle is contained in the radial cluster set of its harmonic component. Comparable results do not hold for ordinary fine cluster sets (or equivalently full-fine cluster sets at the Kuramochi boundary) even when we are dealing with bounded, univalent analytic functions and we are therefore able to answer a question raised by Ohtsuka ([19], p. 295) in the negative.