Corrections to the article On the theory of fractional differentiation and integration of periodic functions belonging to the class $L_p$ , $p>1$ (
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Correction
In the article by I. I. Ogiyevetsky, “On the theory of fractional differentiation and integration of periodic functions belonging to the class \(L_p,\ p>1\),” published in DAN, vol. 118, no. 3, 1958.
| Printed | Should read | |
|---|---|---|
| p. 444, line 6 from below | \(O(1-n^{1-\alpha})\) | \(O(1/n^{1-\alpha})\) |
| p. 445, line 10 | \(0<1+\beta-\gamma<1\) | \(0<1+\beta+\delta-\gamma<1\) |
| p. 445, line 18 | \((f_\gamma)_\delta \subset \operatorname{Lip}(1-\beta-\gamma-\delta,\ p)\) | \((f^\gamma)_\delta \subset \operatorname{Lip}(1-\beta-\gamma+\delta,\ p)\) |
| p. 445, line 20 | \(\alpha+\beta-\dfrac{1}{p}-\dfrac{p}{p'}=1\) | \(\alpha+\beta-\dfrac{1}{p}+\dfrac{1}{p'}=1\) |
| p. 446, line 21 | \(f_\beta(x)\subset \operatorname{Lip}\left(1+\beta-\dfrac{1}{p}-\dfrac{1}{p'},\ p'\right)\) | \(f_\beta(x)\subset \operatorname{Lip}\left(1+\beta-\dfrac{1}{p}+\dfrac{1}{p'},\ p'\right)\) |
| p. 446, line 23 | \(\beta=\dfrac{1}{p}+\dfrac{1}{p'}\) | \(\beta=\dfrac{1}{p}-\dfrac{1}{p'}\) |
| p. 446, line 24 | \(\alpha-\gamma-\dfrac{1}{p}+\dfrac{1}{p'}=0\) | \(\alpha-\gamma-\dfrac{1}{p}+\dfrac{1}{p'}>0\) |
T-08899. Signed for printing 24 IX 1958. Print run 5400 copies. Order 844
Paper size \(70\times108^{1}/_{16}\). Paper sheets \(6^{3}/_{4}\). Printed sheets \(18.5+6\) inserts. Publisher’s sheets 18.7
2nd Printing House of the Publishing House of the Academy of Sciences of the USSR. Moscow, Shubinsky Lane, 10.
Submission history
[v1] 1958-01-01