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On sharpness of growth estimates of Cauchy-Stieltjes integrals
in the unit disc and the polydisc |
| Author |
I. E. Chyzhykov, O. A. Zolota
chyzhykov@yahoo.com, o.zolota@gmail.com
Ivan Franko National University of Lviv, Drohobych Ivan Franko State Pedagogical University
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| Abstract |
The examples showing sharpness of results of M. M. Sheremeta and the second author are
constructed. |
| Keywords |
modulus of continuity; Cantor type function; Cauchy-Stieltjes integral; unit disc; polydisc;
omega-capacity |
| DOI |
doi:10.30970/ms.37.2.155-160
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| Reference |
1. Sheremeta M.M. On the asymptotic behaviour of Cauchy-Stieltjes integrals// Mat. Stud. - 1997. - V.7,
no.2. - P. 175-178.
2. Zolota O.A. On the asymptotic behaviour of Cauchy-Stieltjes integral in the polydisc// Ufimskii Mat.
Jounal. - 2012. - V.4, no.1. - P. 166-172.
3. Salem R. On a theorem of Zygmund// Duke Mathematical Journal. - 1943. - V.10. - P. 23-31.
4. Carleson L. Selected problems on exceptional sets. - Van Nostrand, New York, 1967. - 126 p.
5. Kolmogorov A.N., Fomin S.V. Elements of function theory and functional analysis. - Moscow: Nauka,
1981. - 544 p. (in Russian)
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| Pages |
155-160 |
| Volume |
37 |
| Issue |
2 |
| Year |
2012 |
Journal |
Matematychni Studii |
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