Geodesic
Some families of complex lines of minimal dimension which are sufficient for holomorphic continuation of integrable functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 97-105.

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

In this paper we consider continuous integrable functions given on the boundary of a bounded simply connected domain $D$ of $\mathbb C^n$, $n>1$, and having one-dimensional property of holomorphic extension along the families of complex lines.
Keywords: holomorphic continuation, integrable functions, Bochner–Martinelli integral. 
@article{JSFU_2012_5_1_a10,
     author = {Bairambay P. Otemuratov},
     title = {Some families of complex lines of minimal dimension which are sufficient for holomorphic continuation of integrable functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {97--105},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a10/}
}
TY  - JOUR
AU  - Bairambay P. Otemuratov
TI  - Some families of complex lines of minimal dimension which are sufficient for holomorphic continuation of integrable functions
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2012
SP  - 97
EP  - 105
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a10/
LA  - ru
ID  - JSFU_2012_5_1_a10
ER  - 
%0 Journal Article
%A Bairambay P. Otemuratov
%T Some families of complex lines of minimal dimension which are sufficient for holomorphic continuation of integrable functions
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2012
%P 97-105
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a10/
%G ru
%F JSFU_2012_5_1_a10
Bairambay P. Otemuratov. Some families of complex lines of minimal dimension which are sufficient for holomorphic continuation of integrable functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 97-105. http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a10/

[1] M. L. Agranovskii, R. E. Valskii, “Maksimalnost invariantnykh algebr funktsii”, Sib. matem. zhurn., 12:1 (1971), 3–12 | MR

[2] E. L. Stout, “The boundary values of holomorphic functions of several complex variables”, Duke Math. J., 44:1 (1977), 105–108 | DOI | MR | Zbl

[3] L. A. Aizenberg, A. P. Yuzhakov, Integralnye predstavleniya i vychety v mnogomernom kompleksnom analize, Nauka, Novosibirsk, 1979 | MR

[4] A. M. Kytmanov, Integral Bokhnera–Martinelli i ego primeneniya, Nauka, Novosibirsk, 1992

[5] A. M. Kytmanov, S. G. Myslivets, “Higher-dimensional boundary analogs of the Morera theorem in problems of analytic continuation of functions”, J. Math. Sci., 120:6 (2004), 1842–1867 | DOI | MR | Zbl

[6] J. Globevnik, E. L. Stout, “Boundary Morera theorems for holomorphic functions of several complex variables”, Duke Math. J., 64:3 (1991), 571–615 | DOI | MR | Zbl

[7] A. M. Kytmanov, S. G. Myslivets, “O semeistvakh kompleksnykh pryamykh, dostatochnykh dlya golomorfnogo prodolzheniya”, Matem. zametki, 83:4 (2008), 545–551 | MR | Zbl

[8] B. P. Otemuratov, “O funktsiyakh klassa $L^p$ so svoistvom odnomernogo golomorfnogo prodolzheniya”, Vestnik KrasGU. Ser. fiz. mat. nauki (Krasnoyarsk), 2006, no. 9, 95–100

[9] B. P. Otemuratov, “O mnogomernykh teoremakh Morera dlya integriruemykh funktsii”, Uzb. mat. zhurnal (Tashkent), 2009, no. 2, 129–134 | MR

[10] A. M. Kytmanov, S. G. Myslivets, V. I. Kuzovatov, “Semeistva kompleksnykh pryamykh minimalnoi razmernosti, dostatochnye dlya golomorfnogo prodolzheniya funktsii”, Sib. mat. zhurnal, 52:2 (2011), 326–339 | MR | Zbl