Geodesic
Generalized Variation and Functions of Slow Growth
Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 55-85

Voir la notice de l'article provenant de la source Cambridge University Press

Many of the basic results of HP theory on the disk Δ = {|z| < 1} are proved using the Cauchy-Stieltjes representation 1.1 and the Poisson-Stieltjes representation 1.2 Here, μ:R → C is a complex-valued function of a real variable that is of bounded variation on [0, 2π] such that μ(t + 2π) = μ(t) + μ(2t) — μ(0), t ∊ R, is the Cauchy kernel, and is the Poisson kernel. It is therefore natural to generalize these representations in such a way that some of the basic properties and results carry over. Such a generalization occurs when the assumption that μ is of bounded variation on [0, 2μ] is replaced by the requirement that it is measurable and bounded on [0, 2μ] (cf. [9]). The integrals in (1.1) and (1.2) are then defined by a formal integration by parts. After some preliminaries in Section 2, we catalogue a variety of results which remain valid in Section 3. 
Berman, Robert D. Generalized Variation and Functions of Slow Growth. Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 55-85. doi: 10.4153/CJM-1988-003-7
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