Geodesic
Comparison of Two Generalized Trigonometric Integrals
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 278-287 
V. A. Skvortsov; N. N. Kholshchevnikova. Comparison of Two Generalized Trigonometric Integrals. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 278-287. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a10/
@article{MZM_2006_79_2_a10,
     author = {V. A. Skvortsov and N. N. Kholshchevnikova},
     title = {Comparison of {Two} {Generalized} {Trigonometric} {Integrals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {278--287},
     year = {2006},
     volume = {79},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a10/}
}
TY  - JOUR
AU  - V. A. Skvortsov
AU  - N. N. Kholshchevnikova
TI  - Comparison of Two Generalized Trigonometric Integrals
JO  - Matematičeskie zametki
PY  - 2006
SP  - 278
EP  - 287
VL  - 79
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a10/
LA  - ru
ID  - MZM_2006_79_2_a10
ER  - 
%0 Journal Article
%A V. A. Skvortsov
%A N. N. Kholshchevnikova
%T Comparison of Two Generalized Trigonometric Integrals
%J Matematičeskie zametki
%D 2006
%P 278-287
%V 79
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a10/
%G ru
%F MZM_2006_79_2_a10

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

The $P^2$-integral of James is compared with the $T^2$-integral. A trigonometric series convergent almost everywhere to a function which is $T^2$-integrable but not $P^2$-integrable is constructed.

[1] Vinogradova I. A., Skvortsov V. A., “Obobschennye integraly i ryady Fure”, Itogi nauki i tekhn. Matem. analiz 1970, VINITI, Moskva, 1971, 65–107 | MR | Zbl

[2] James R. D., “A generalized integral, II”, Canad. J. Math., 1950, no. 3, 297–306 | MR | Zbl

[3] Kholschevnikova N. N., “Obobschennyi trigonometricheskii integral”, Izv. NAN Armenii. Ser. matem., 36:4 (2001), 82–89 | MR

[4] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[5] Skvortsov V. A., “Svyaz mezhdu nekotorymi integralami”, Vestn. MGU. Ser. 1. Matem., mekh., 1967, no. 4, 68–71

[6] Sklyarenko V. A., “Ob integrirovanii po chastyam v SCP-integrale Berkillya”, Matem. sb., 112 (154):4 (8) (1980), 630–646 | MR | Zbl