Keywords: Analytic function; area Nevanlinna type spaces; zero sets; factorization representation; meromorphic function; subharmonic function.
@article{COMIM_2018_26_1_a4,
author = {Shamoyan, Romi and Maksakov, Seraphim},
title = {Area {Nevanlinna} type classes of analytic functions in the unit disk and related spaces},
journal = {Communications in Mathematics},
pages = {47--76},
year = {2018},
volume = {26},
number = {1},
mrnumber = {3827143},
zbl = {1404.30061},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2018_26_1_a4/}
}
TY - JOUR AU - Shamoyan, Romi AU - Maksakov, Seraphim TI - Area Nevanlinna type classes of analytic functions in the unit disk and related spaces JO - Communications in Mathematics PY - 2018 SP - 47 EP - 76 VL - 26 IS - 1 UR - http://geodesic.mathdoc.fr/item/COMIM_2018_26_1_a4/ LA - en ID - COMIM_2018_26_1_a4 ER -
Shamoyan, Romi; Maksakov, Seraphim. Area Nevanlinna type classes of analytic functions in the unit disk and related spaces. Communications in Mathematics, Tome 26 (2018) no. 1, pp. 47-76. http://geodesic.mathdoc.fr/item/COMIM_2018_26_1_a4/
[1] Avetisyan, K.: On representation of some classes of subharmonic functions in the unit disk and in the half plane. Izv. Nats. Acad. Armenii, Matematika., 29, 1, 1994, 1-13, (In Russian). | MR
[2] Bednazh, V.A., Karbanovich, O.V., Shamoyan, F.A.: On some weighted spaces of meromorphic functions with restrictions of the Nevanlinna characteristic. Modern problems of complex and harmonic analysis: Abstracts of conference, Bryansk St. Univ., 2014, p. 56, (In Russian).
[3] Beller, E.: Zeros of $A^p$ functions and related classes of analytic functions. Israel Jour. Math., 22, 1975, 68-80, 1. | DOI | MR
[4] Beller, E.: Factorization for non-Nevanlinna classes of analytic functions. Israel Jour. Math., 27, 3--4, 1977, 320-330, | MR
[5] Chyzhykov, I.E.: Growth of analytic functions in the unit disc and complete measure in the sense of Grishin. Mat. Stud., 29, 1, 2008, 35-44, | MR
[6] Chyzhykov, I.E.: Zero distribution and factorization of analytic functions of slow growth in the unit disc. Proc. Amer. Math. Soc., 141, 2013, 1297-1311, | DOI | MR
[7] Chyzhykov, I.E.: Growth of $p$-th means of analytic and subharmonic function in the unit disk and angular distribution of zeros. arXiv:1509.02141, 2015, 1-19, | MR
[8] Chyzhykov, I.E., Skaski, S.: Growth, zero distribution and factorization of analytic functions of moderate growth in the unit disc, Blashke products and their applications. Fields Inst. Comm., 65, 2013, 159-173, | MR
[9] Djrbashian, M.M.: On a problem of representation of analytic functions. Soobsch. Inst. Mat. i Meh. AN Arm. SSR, 2, 1948, 3-40, (In Russian).
[10] Djrbashian, M.M.: On parametric representation of some classes of meromorphic functions in the unit disk. Dokl. AN SSSR., 157, 1964, 1024-1027, (in Russian).
[11] Djrbashian, M.M.: Integral transforms and representation in complex plane. 1966, p. 671, Nauka, GITTL. Moscow, (In Russian).
[12] Djrbashian, M.M.: The factorization theory of functions, meromorphic in the unit disk. Mat. Sb., 79, 121, 1969, 517-615, (In Russian).
[13] Djrbashian, A.M., Mikaelyan, G.V.: On boundary properties of Blaschke type products. Izv. Nats. AN Armenii, Matematika, 26, 1991, 435-442, (In Russian). | MR
[14] Goldberg, A.A., Ostrovskii, I.V.: On distribution of values of meromorphic functions. 1970, p. 457, Nauka. Moscow, (In Russian). | MR
[15] Hardy, G., Littlwood, J., Polia, G.: Inequalities. 1948, p. 456, GITTL, Moscow, (In Russian). | MR
[16] Hayman, W.: Meromorphic functions. 1966, p. 447, Mir, Moscow, (In Russian). | MR
[17] Heipler, A.: The zeros of functions in Nevanlinna's area class. Israel Jour. Math., 34, 1--2, 1979, 1-11, | DOI | MR
[18] Kasyaniuk, S.Ya.: On functions from $A$ and $H$ class in case of circular rings. Mat. Sb., 42, 84, 1957, 301-326, (In Russian).
[19] Krylov, V.I.: On functions regular in half plane. Mat. Sb., 6, 48, 1939, 95-138, (In Russian).
[20] Kursina, I.S.: Factorization and parametric representation of weighted classes of analytic functions: the thesis abstract. Voronezh State Univ., Voronezh, 4, 2000, 43-54, (In Russian).
[21] Matevosyan, G.U.: On an factorization of functions meromorphic in multiconnected domains and applications. Izv. AN Armenii, Matematika, 9, 1974, 387-408, (In Russian).
[22] Matevosyan, G.U.: An analogue of $N(w)$ class in case of circular rings. Izv. AN Armenii, Matematika., 21, 2, 1977, 173-182, (In Russian).
[23] Nevanlinna, R.: Single-Valued Analytic Functions. 1941, p. 388, Gostehizdat, Moscow, (In Russian).
[24] Ohlupina, O.V.: Description of a class of subharmonic functions in the unit disk, whose Nevanlinna's characteristic is in wheigted $L^p$-spaces. Vestnik Samarskogo Univ., 9/1, 59, 2008, 108-120, (In Russian). | MR
[25] Ohlupina, O.V.: Parametric representation of some classes of subharmonic functions in a half plane with characteristic from weighted $L^p$-spaces. Vestnik Bryanskogo Univ., Bryansk State Univ., 4, 2010, 24-36, (In Russian).
[26] Ohlupina, O.V.: Green type potentials and integral representation of wheigted classes of subharmonic functions: the PhD thesis abstract. 38, 2012, 56-77, Saratov St. Univ., Saratov, (In Russian).
[27] Ortega-Cerda, J., Bruna, J.: On $L^p$-solutions of the Laplace equation and zeros of holomorphic functions. Annali della Scuola Normale de Pisa, 24, 1997, 571-591, | MR
[28] Prihodko, O.V.: On root sets of some area Nevanlinna type spaces in angular domains on a complex plane. Vestnik Bryanskogo Univ. Bryansk State Univ., Bryansk, 4, 2010, 36-40, (In Russian).
[29] Privalov, I.I.: Boundary properties of single-valued analytic functions. 1941, 206 p., Moscow St. Univ., Moscow, (In Russian). | MR
[30] Privalov, I.I.: Boundary properties of analytic functions. 1950, 337 p., Gostekhizdat, Moscow and Leningrad, (In Russian). | MR
[31] Privalov, I.I., Kuznetsov, P.I.: Boundary properties and various classes of harmonic and subharmonic functions, defined in arbitrary domains. Mat. Sbornik, 6, 48, 1939, 345-376, (In Russian).
[32] Rodikova, E.G.: Factorization and description of zero sets of a class of functions, analytic in the unit disk. Sib. Elektron. Mat. Izv., 11, 2014, 52-63, (In Russian). | MR
[33] Rodikova, E.G.: Factorization, root sets and interpolation in weighted classes of analytic functions. 2014, 121 p., Bryansk, Dissertation, Bryansk, (2014) ,121 p. (In Russian).
[34] Rodikova, E.G.: On zeros of analytic classes of Privalov. Abstracts of Saratov winter school, Saratov, 1, 39, 2012, 141-142, (In Russian).
[35] Seneta, E.: Regularly varying functions. 1985, 141 p., Nauka, Moscow, (In Russian). | MR
[36] Shamoyan, F.A.: Description of closed ideals and some issues of factorization in algebras of growing functions, analytic in the disk. Izv. Acad. nauk ArmSSR, Matematika, 5, 1970, 450-472, (In Russian). | MR
[37] Shamoyan, F.A.: Djrbashian's factorization theorem and characterization of zeros of analytic functions in a disk with bounded growth rate. Izv. Acad. nauk ArmSSR, Matematika, 13, 1978, 405-422, (In Russian).
[38] Shamoyan, F.A.: Some remarks to parametric representation of Nevanlinna-Djrbashian. Mat. zametki., 52, 1992, 128-140, (In Russian).
[39] Shamoyan, F.A.: Parametric representation and description of zero sets of weighted classes of holomorphic functions in the disk. Sib. Math. Journ., 40, 1999, 1422-1440, (In Russian). | DOI | MR
[40] Shamoyan, F.A.: Weighted spaces of analytic functions with mixed norm. 2014, 250 p., Bryansk St. Univ., Bryansk, Bryansk State University Publishing House, (In Russian).
[41] Shamoyan, F.A., Bednazh, V.A., Karbanovich, O.V.: On classes of analytic functions in a disk with a characteristic R. Nevanlinny and $\alpha $-characteristic of weighted $L^p$ spaces. Sib. Elektron. Mat. Izv., 12, 2015, 150-167, (In Russian). | MR
[42] Shamoyan, F.A., Bednazh, V.A., Prihodko, O.V.: On zero sets of some weighted classes of analytc functions in the disk. Vesthik Bryanskogo Universiteta, Bryansk, 4, 2008, 85-92, (In Russian).
[43] Shamoyan, F.A., Rodikova, E.G.: On characterization of root sets of a weighted class of analytic functions in a disk. Vladikavkaz Mat. Jour., 16, 3, 2014, 64-75, (In Russian). | MR
[44] Shamoyan, F.A., Shubabko, E.N.: Parametrical representations of some classes of holomorfic functions in the disc. Complex Analysis, Operators, and Related Topics, Oper. Theory Adv. Appl, 113, 2000, 331-338, (In Russian). | DOI | MR
[45] Shamoyan, F.A., Shubabko, E.N.: On a class of holomorphic functions in a disk. Zapiski Nauchnykh Seminarov POMI., 282, 2001, 244-255, (In Russian). | MR
[46] Shamoyan, F.A., Shubabko, E.N.: Introduction in the theory of $L^p$-classes of meromorphic functions. 2009, 152 p, Bryansk State University Publishing House, (In Russian).
[47] Shamoyan, R.F.: On new parametric representations of analytic area Nevanlinna type classes in a circular ring $K$ on a complex plane $\mathbb {C}$. Jour. Sib. Fed. Univ. Math. Phys., 6, 1, 2013, 114-119, | MR
[48] Shamoyan, R.F., Li, H.: Descriptions of zero sets and parametric representations of certain new analytic area Nevanlinna type spaces in the unit disk. Kragujevac Journal of Mathematics, 34, 2010, 73-89, | MR
[49] Shamoyan, R.F., Mihic, O.R.: On zeros of some analytic spaces of area Nevanlinna type in halfplane. Trudy Petrozavodsk St. Univ., Matematika., 17, 2010, 67-72, | MR
[50] Shamoyan, R.F., Mihic, O.R.: On some new theorems on certain analytic and meromorphic classes of Nevanlinna type on the complex plane. Kragujevac Math. Journal, 37, 1, 2013, 65-85, | MR
[51] Shamoyan, R.F., Mihic, O.R.: On zeros sets and embeddings of some new analytic function spaces in the unit disk. Kragujevac Math. Journal, 38, 2, 2014, 229-244, | DOI | MR
[52] Shamoyan, R., Shipka, A.: Integral operators, embedding theorems and Taylor coefficients of area Nevanlinna type spaces of several variables and related problems. 2018, Preprint..
[53] Shvedenko, S.V.: Canonical products of Blashke type for spaces of area Nevanlinna type. Mat. Zametki., 37, 2, 1985, 212-219, (In Russian). | MR
[54] Shvedenko, S.V.: The Hardy classes and related spaces of analytic functions in the unit circle, in the ball and in the polydisk. Itogi nauki i tehniki, Mat. analiz., 23, 1985, 3-124, | MR
[55] Stein, E.: Singular integrals and differentiability properties of functions. 1970, 290 p., Princeton Univ. Press, New Jersey, | MR | Zbl
[56] Tsuji, M.: Canonical product for a meromorphic functions in a unit circle. Journ. Math. Jap., 8, 1, 1956, 7-19, | MR
[57] Tsuji, M.: Potential Theory in modern function theory. 1959, p. 345, Maruzen, Tokyo, | MR
[58] Zmorovich, V.: On certain spaces of analytic functions in circular rings. Mat. Sbornik, 32, 1953, 643-652, (In Russian). | MR