The Stieltjes integrals in the theory of harmonic and analytic functions

Autor:	Ryazanov, Vladimir
Rok vydání:	2017
Předmět:	Mathematics - Complex Variables Primary 30C62 31A05 31A20 31A25 31B25 Secondary 30E25 31C05 34M50 35F45 35Q15
Druh dokumentu:	Working Paper
Popis:	We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular Hilbert-Stieltjes integral in the sense of the principal value. These results hold for arbitrary $2\pi -$periodic bounded integrands that are differentiable a.e. and, in particular, for integrands of the class ${\cal {CBV}}$ (countably bounded variation). Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.02717 Zobrazit plný text záznamu View this record from Arxiv