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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 {\textquotedblleft}$J_k${-Lacunary} {Sequence} of {Partial} {Sums{\textquotedblright}} in {Orlicz} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {26--36},
     year = {2014},
     volume = {95},
     number = {1},
     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
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
%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/

[1] I. L. Bloshanskii, “O kriteriyakh slaboi obobschennoi lokalizatsii v $n$-mernom prostranstve”, Dokl. AN SSSR, 271:6 (1983), 1294–1298 | MR | Zbl

[2] I. L. Bloshanskii, O. V. Lifantseva, “Slabaya obobschennaya lokalizatsiya dlya kratnykh ryadov Fure, pryamougolnye chastichnye summy kotorykh rassmatrivayutsya po nekotoroi podposledovatelnosti”, Matem. zametki, 84:3 (2008), 334–347 | DOI | MR | Zbl

[3] I. L. Bloshanskii, O. V. Lifantseva, “O lokalizatsii dlya kratnykh ryadov Fure s lakunarnoi posledovatelnostyu chastichnykh summ v klasse $L_1$”, Materialy 15-i Saratovskoi zimnei shkoly, Izd-vo SGU, Saratov, 2010, 29–30

[4] I. Bloshanskii, O. Lifantseva, Z. Tsukareva, “On localization for multiple Fourier series with lacunary sequences of partial sums in Orlicz spaces”, The 8-th Congress of the International Society for Analysis, its Applications, and Computations, Peoples' Friendship University of Russia, Moscow, 2011, 399–400

[5] Z. N. Tsukareva, “Slabaya obobschennaya lokalizatsiya dlya kratnykh ryadov Fure s lakunarnoi posledovatelnostyu chastichnykh summ v klassakh Orlicha”, Vestn. Mosk. gos. obl. un-ta. Ser. Fiz., matem., 2012, no. 1, 18–22, M.

[6] R. A. Hunt, “On the convergence of Fourier series”, Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967), Southern Illinois Univ. Press, Carbondale, Ill, 1968, 235–255 | MR | Zbl

[7] D. K. Sanadze, Sh. V. Kheladze, “O skhodimosti i raskhodimosti kratnykh ryadov Fure–Uolsha”, Tr. Tbilissk. matem. in-ta AN Gruz. SSR, 55, 1977, 93–106 | MR | Zbl

[8] I. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[9] H. Whitney, “Analytic extensions of differentiable functions defined in closed sets”, Trans. Amer. Math. Soc., 36:1 (1934), 63–89 | DOI | MR | Zbl