Geodesic
Localization for Multiple Fourier Series with ``$J_k$-Lacunary Sequence of Partial Sums'' in Orlicz Classes
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 26-36

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

We obtain structural and geometric characteristics of sets on which weak generalized localization almost everywhere is valid for multiple trigonometric Fourier series of functions in the classes $L(\log^+L)^{3k+2}(\mathbb T^N)$, $1\le k\le N-2$, $N\ge 3$, in the case where the rectangular partial sums of these series have a “number” in which exactly $k$ components are terms of lacunary sequences.
Keywords: trigonometric Fourier series, lacunary sequence of partial sums, localization for Fourier series, Orlicz class of functions
Mots-clés : Lebesgue measure. 
@article{MZM_2014_95_1_a2,
     author = {I. L. Bloshanskii and Z. N. Tsukareva},
     title = {Localization for {Multiple} {Fourier} {Series} with ``$J_k${-Lacunary} {Sequence} of {Partial} {Sums''} in {Orlicz} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {26--36},
     publisher = {mathdoc},
     volume = {95},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a2/}
}
TY  - JOUR
AU  - I. L. Bloshanskii
AU  - Z. N. Tsukareva
TI  - Localization for Multiple Fourier Series with ``$J_k$-Lacunary Sequence of Partial Sums'' in Orlicz Classes
JO  - Matematičeskie zametki
PY  - 2014
SP  - 26
EP  - 36
VL  - 95
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a2/
LA  - ru
ID  - MZM_2014_95_1_a2
ER  - 
%0 Journal Article
%A I. L. Bloshanskii
%A Z. N. Tsukareva
%T Localization for Multiple Fourier Series with ``$J_k$-Lacunary Sequence of Partial Sums'' in Orlicz Classes
%J Matematičeskie zametki
%D 2014
%P 26-36
%V 95
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a2/
%G ru
%F MZM_2014_95_1_a2
I. L. Bloshanskii; Z. N. Tsukareva. Localization for Multiple Fourier Series with ``$J_k$-Lacunary Sequence of Partial Sums'' in Orlicz Classes. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 26-36. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a2/