Geodesic
Comparison of Some Trigonometric Integrals
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 301-308.

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that Preiss–Thomson's AS-integral is inconsistent with Burkill's SCP-integral, James' $\mathrm P^2$-integral, and Denjoy's totalization $\mathrm{T}_{2s}$ over the class of functions with continuous primitives.
Keywords: symmetric Cesàro derivative, approximate symmetric derivative, Denjoy's totalization $\mathrm T_{2s}$, Burkill's SCP-integral, Preiss–Thomson's AS-integral, James' $\mathrm P^2$-integral. 
@article{MZM_2018_104_2_a12,
     author = {P. A. Sworovsky and V. A. Skvortsov},
     title = {Comparison of {Some} {Trigonometric} {Integrals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {301--308},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a12/}
}
TY  - JOUR
AU  - P. A. Sworovsky
AU  - V. A. Skvortsov
TI  - Comparison of Some Trigonometric Integrals
JO  - Matematičeskie zametki
PY  - 2018
SP  - 301
EP  - 308
VL  - 104
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a12/
LA  - ru
ID  - MZM_2018_104_2_a12
ER  - 
%0 Journal Article
%A P. A. Sworovsky
%A V. A. Skvortsov
%T Comparison of Some Trigonometric Integrals
%J Matematičeskie zametki
%D 2018
%P 301-308
%V 104
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a12/
%G ru
%F MZM_2018_104_2_a12
P. A. Sworovsky; V. A. Skvortsov. Comparison of Some Trigonometric Integrals. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 301-308. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a12/

[1] A. Zigmund, Trigonometricheskie ryady, T. 1, 2, Mir, M., 1965 | MR | Zbl | Zbl

[2] A. Denjoy, Leçons sur le calcul des coefficients d'une série trigonometrique, Gauthier-Villars, Paris, 1941 | MR | Zbl

[3] J. Marcinkiewicz, A. Zygmund, “On the differentiability of functions and summability of trigonometrical series”, Fund. Math., 26 (1936), 1–43 | DOI | Zbl

[4] R. D. James, “A generalized integral. II”, Canadian J. Math., 2 (1950), 297–306 | DOI | MR | Zbl

[5] J. C. Burkill, “Integrals and trigonometrical series”, Proc. London Math. Soc. (3), 1 (1951), 46–57 | DOI | MR | Zbl

[6] V. A. Skvortsov, N. N. Kholschevnikova, “Sravnenie dvukh obobschennykh trigonometricheskikh integralov”, Matem. zametki, 79:2 (2006), 278–287 | DOI | MR | Zbl

[7] V. A. Skvortsov, “Vzaimosvyaz mezhdu $AP$-integralom Teilora $P^2$-integralom Dzheimsa”, Matem. sb., 70 (112):3 (1966), 380–393 | MR | Zbl

[8] V. A. Skvortsov, F. Tulone, “Obobschennye integraly Khenstoka v teorii ryadov po multiplikativnym sistemam”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2004, no. 2, 7–11 | MR | Zbl

[9] T. P. Lukashenko, V. A. Skvortsov, A. P. Solodov, Obobschennye integraly, URSS, M., 2010

[10] V. A. Skvortsov, “Henstock integral in harmonic analysis”, Sci. Math. Jpn., 67:1 (2008), 71–82 | MR | Zbl

[11] V. A. Skvortsov, F. Tulone, “Kurzweil–Henstock type integral on zero-dimensional group and some of its applications”, Czechoslovak Math. J., 58:4 (2008), 1167–1183 | DOI | MR | Zbl

[12] V. A. Skvortsov, F. Tulone, “$\mathcal P$-ichnyi integral Khenstoka v teorii ryadov po sistemam kharakterov nul-mernykh grupp”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2006, no. 1, 25–29 | MR | Zbl

[13] D. Preiss, B. S. Thomson, “The approximate symmetric integral”, Canadian J. Math., 41:3 (1989), 508–555 | DOI | MR | Zbl

[14] B. S. Thomson, Symmetric Properties of Real Functions, Monogr. Textbooks Pure Appl. Math., 183, Marcel Dekker, New York, 1994 | MR | Zbl

[15] V. A. Skvortsov, “Approksimativnaya simmetricheskaya variatsiya i $N$-svoistvo Luzina”, Izv. RAN. Ser. matem., 61:4 (1997), 155–166 | DOI | MR | Zbl