Ces\`aro means for the functions from the Hardy space in polydisc
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 55-59.

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

We prove that Cesàro mean values of analytic functions in the unit polydisc in a Hardy space are bounded with respect to the parameter $m$, provided that the rest parameters satisfy certain conditions.
Keywords: polydisc, Hardy class in polydisc, Cesàro means.
@article{IVM_2015_4_a5,
     author = {S. G. Pribegin},
     title = {Ces\`aro means for the functions from the {Hardy} space in polydisc},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--59},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_4_a5/}
}
TY  - JOUR
AU  - S. G. Pribegin
TI  - Ces\`aro means for the functions from the Hardy space in polydisc
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 55
EP  - 59
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_4_a5/
LA  - ru
ID  - IVM_2015_4_a5
ER  - 
%0 Journal Article
%A S. G. Pribegin
%T Ces\`aro means for the functions from the Hardy space in polydisc
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 55-59
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2015_4_a5/
%G ru
%F IVM_2015_4_a5
S. G. Pribegin. Ces\`aro means for the functions from the Hardy space in polydisc. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 55-59. http://geodesic.mathdoc.fr/item/IVM_2015_4_a5/

[1] Bochner S., “Boudary values of analytic functions of several variables and of almost periodic functions”, Ann. Math., 45:4 (1944), 708–722 | DOI | MR | Zbl

[2] Rudin U., Teoriya funktsii v polikruge, Mir, M., 1974 | MR | Zbl

[3] Storozhenko E. A., “Priblizhenie funktsii klassa $H^p$, $0

\le1$”, Matem. sb., 105(147):4 (1978), 601–621 | MR | Zbl

[4] Volashek Ya., “O priblizhenii v mnogomernykh prostranstvakh Khardi $H^p$, $0

\le1$”, Soobsch. AN GSSR, 105:1 (1982), 21–24 | MR

[5] Weisz Ferenc, “Cesàro-summability of higher-dimensional Fourier series”, Ann. Univ. Sci. Budapest, Sect. Comp., 37 (2012), 47–64 | MR | Zbl

[6] Pribegin S. G., “O nekotorykh metodakh summirovaniya stepennykh ryadov dlya funktsii iz $H^p(D^n)$, $0

\infty$”, Matem. sb., 200:2 (2009), 89–106 | DOI | MR | Zbl

[7] Hardy G. H., Littlewood J. E., “Some properties of fractional integrals. II”, Math. Zeit., 34:3 (1932), 403–439 | DOI | MR

[8] Duren P. L., Theory of $H^p$-spaces, Academic Press, New York–London, 1970 | MR | Zbl

[9] Frazier A. P., “The dual space of $H^p$ of the polydisc for $0

1$”, Duke Math. J., 39:2 (1972), 369–379 | DOI | MR | Zbl

[10] Khardi G. G., Raskhodyaschiesya ryady, In. lit., M., 1951

[11] Bari N. K., Trigonometricheskie ryady, GIFML, M., 1961 | MR