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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 |
| Reference |
1. Sheremeta M.M. On the asymptotic behaviour of Cauchy-Stieltjes integrals// Mat. Stud. – 1997. – V.7,
¹2. – P. 175–178.
2. Zolota O.A. On the asymptotic behaviour of Cauchy-Stieltjes integral in the polydisc// Ufimskii Mat.
Jounal. – 2012. – V.4, ¹1. – 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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