Geodesic
Multiplicative Bounds for $L_1$-Norms of Exponential Sums
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 49-57.

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

This paper is a sequel of the author's papers [1]–[8] devoted to lower multiplicative bounds on $L_1$ norms and their applications. Now we give estimates for $L_1$ norms of exponential sums and prove the result announced in the paper [8]. 
@article{CMFD_2007_25_a4,
     author = {S. V. Bochkarev},
     title = {Multiplicative {Bounds} for $L_1${-Norms} of {Exponential} {Sums}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {49--57},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_25_a4/}
}
TY  - JOUR
AU  - S. V. Bochkarev
TI  - Multiplicative Bounds for $L_1$-Norms of Exponential Sums
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2007
SP  - 49
EP  - 57
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2007_25_a4/
LA  - ru
ID  - CMFD_2007_25_a4
ER  - 
%0 Journal Article
%A S. V. Bochkarev
%T Multiplicative Bounds for $L_1$-Norms of Exponential Sums
%J Contemporary Mathematics. Fundamental Directions
%D 2007
%P 49-57
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2007_25_a4/
%G ru
%F CMFD_2007_25_a4
S. V. Bochkarev. Multiplicative Bounds for $L_1$-Norms of Exponential Sums. Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 49-57. http://geodesic.mathdoc.fr/item/CMFD_2007_25_a4/

[1] Bochkarev S. V., “Absolyutnaya skhodimost ryadov Fure po polnym ortonormirovannym sistemam”, UMN, 27:2 (1972), 53–76 | MR | Zbl

[2] Bochkarev S. V., “O probleme Zigmunda”, Izv. AN SSSR. Ser. matem., 37:3 (1973), 630–638 | MR | Zbl

[3] Bochkarev S. V., “Ob absolyutnoi skhodimosti ryadov Fure po ogranichennym polnym ortonormirovannym sistemam funktsii”, Matem. sb., 93(135):2 (1974), 203–217 | Zbl

[4] Bochkarev S. V., “Logarifmicheskii rost srednikh arifmeticheskikh ot funktsii Lebega ogranichennykh ortonormirovannykh sistem”, Dokl. AN SSSR, 223:1 (1975), 16–19 | MR | Zbl

[5] Bochkarev S. V., “Raskhodyaschiisya na mnozhestve polozhitelnoi mery ryad Fure dlya proizvolnoi ogranichennoi ortonormirovannoi sistemy”, Matem. sb., 98(140):3 (1975), 436–449 | MR | Zbl

[6] Bochkarev S. V., Metod usrednenii v teorii ortogonalnykh ryadov i nekotorye voprosy teorii bazisov, Trudy MIAN, 146, 1978 | MR | Zbl

[7] Bochkarev S. V., “Ryady Valle Pussena v prostranstvakh $\mathrm{BMO}$, $L_1$i $H^1(D)$ i multiplikativnye neravenstva”, Trudy MIAN, 210, 1995, 41–64 | MR | Zbl

[8] Bochkarev S. V., “Ob odnom metode otsenki $L_1$-normy eksponentsialnoi summy”, Trudy MIAN, 218, 1997, 74–76 | MR | Zbl

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

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

[11] Karatsuba A. A., “Ob otsenke $L_1$-normy odnoi eksponentsialnoi summy”, Matem. zametki, 64:3 (1998), 465–468 | MR | Zbl

[12] Konyagin S. V., “O probleme Littlvuda”, Izv. AN SSSR. Ser. matem., 45:2 (1981), 243–265 | MR | Zbl

[13] Mc Gehee O., Pigno L., Smith B., “Hardy's inequality and the $L_1$ norm of exponential sums”, Ann. of Math. (2), 113:3 (1981), 613–618 | DOI | MR

[14] Rudin W., Function theory in polydiscs, Benjamin, New York, 1969 | MR | Zbl

[15] Yano S., “On a lemma of Marcinkiewicz and its applications to Fourier series”, Tôhoku Math. J. (2), 11 (1959), 191–215 | DOI | MR | Zbl