On the asymptotic behaviour of
Cauchy-Stieltjes integrals

M.M.~Sheremeta

The asymptotic behaviour of analytic in the unit disc function $f(z)\!=\!\int\limits_{-\pi}^\pi \frac{dg(t)}{(1-ze^{-it})^{\alpha}}$, where $g$ is a complex-valued function of bounded variation, is studied.

1. Hallenbeck D.J., MacGregor T.H. Radial limits and radial growth of Cauchy-Stieltjes transforms // Complex Variables. 1993. V.21. P.219–229.

2. Hallenbeck D.J., MacGregor T.H. Radial growth and exceptional sets for Cauchy-Stieltjes integrals // Proc. Edinburgh Math. Soc. 1993. V.37. P.73–89.

3. Дзядык В.К. Введение в теорию равномерной аппроксимации функций полиномами. --- М.: Наука. 1977. 512 с.

4. Twomey J.B. Tangential boundary behaviour of the integral // J. London Math. Soc. 1988. V.37. P.447–454.

	On the asymptotic behaviour of Cauchy-Stieltjes integrals
Author	M.M.~Sheremeta Lviv University, Department of Mechanics and Mathematics
Abstract	The asymptotic behaviour of analytic in the unit disc function $f(z)\!=\!\int\limits_{-\pi}^\pi \frac{dg(t)}{(1-ze^{-it})^{\alpha}}$, where $g$ is a complex-valued function of bounded variation, is studied.
Keywords	analytic function, unit disc, asymptotic behaviour
DOI	doi:10.30970/ms.7.2.175-178
Reference	1. Hallenbeck D.J., MacGregor T.H. Radial limits and radial growth of Cauchy-Stieltjes transforms // Complex Variables. 1993. V.21. P.219–229. 2. Hallenbeck D.J., MacGregor T.H. Radial growth and exceptional sets for Cauchy-Stieltjes integrals // Proc. Edinburgh Math. Soc. 1993. V.37. P.73–89. 3. Дзядык В.К. Введение в теорию равномерной аппроксимации функций полиномами. --- М.: Наука. 1977. 512 с. 4. Twomey J.B. Tangential boundary behaviour of the integral // J. London Math. Soc. 1988. V.37. P.447–454.
Pages	175-178
Volume	7
Issue	2
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On the asymptotic behaviour of Cauchy-Stieltjes integrals