Stieltjes Integrals in the Theory of Harmonic Functions

Resumo

We study various Stieltjes integrals (Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz– Stieltjes, and Cauchy–Stieltjes integrals) and prove theorems on the existence of their finite angular limits a.e. in terms of the Hilbert–Stieltjes integral. These results are valid for arbitrary bounded integrands that are differentiable a.e. and, in particular, for integrands from the class CBV (countably bounded variation).