New classes of function spaces and singular operators
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 2, pp. 329-348.

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     title = {New classes of function spaces and singular operators},
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G. G. Kazaryan; A. N. Karapetyants; V. N. Margaryan; H. A. Mkrtchyan; A. G. Sergeev. New classes of function spaces and singular operators. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 2, pp. 329-348. http://geodesic.mathdoc.fr/item/MMO_2021_82_2_a2/

[1] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, Fizmatlit, M., 1996 | MR

[2] Kazaryan G. G., Karapetyan G. A., “Skhodimost galerkinskikh priblizhenii k resheniyu zadachi Dirikhle dlya nekotorykh neellipticheskikh uravnenii”, DAN SSSR, 264:2 (1982), 291–294 | MR | Zbl

[3] Kazaryan G. G., Karapetyan G. A., “O skhodimosti galerkinskikh priblizhenii k resheniyu zadachi Dirikhle dlya nekotorykh obschikh uravnenii”, Matem. sb., 124 (166):3 (7) (1984), 291–306 | MR | Zbl

[4] Karapetyan G. A., “Reshenie poluellipticheskikh uravnenii v poluprostranstve”, Tr. MIAN SSSR, 170, 1984, 119–138 | Zbl

[5] Karapetyan G. A., “O stabilizatsii v beskonechnosti k polinomu reshenii odnogo klassa regulyarnykh uravnenii”, Tr. MIAN SSSR, 187 (1989), 116–129

[6] Karapetyan G. A., “Integralnoe predstavlenie i teoremy vlozheniya dlya $n$-mernykh multianizotropnykh prostranstv s odnoi vershinoi anizotropnosti”, Sib. matem. zhurn, 58:3 (2017), 573–590 | MR | Zbl

[7] Karapetyan G. A., “Drobnye multianizotropnye prostranstva i teoremy vlozheniya”, Matem. tr., 22:2 (2019), 76–89 | MR

[8] G. A. Karapetyan, M. K. Arakelyan, “Teoremy vlozheniya dlya obschikh multianizotropnykh prostranstv”, Matem. zametki, 104:3 (2018), 422–438 | MR | Zbl

[9] Karapetyan G. A., Dallakyan G. V., “Approksimatsiya reshenii poluellipticheskikh uravnenii v $\mathbb{R}^n$”, Izv. NAN Armenii. Mat., 34:4 (1999), 31–43 | MR | Zbl

[10] Karapetyan G. A., Darbinyan A. A., “Ob indekse poluellipticheskogo operatora v $\mathbb{R}^n$”, Izv. NAN Armenii. Matem., 42:5 (2007), 33–50 | MR | Zbl

[11] Karapetyan G. A., Darbinyan A. A., “Neterovost poluellipticheskogo operatora s postoyannymi koeffitsientami v oblasti”, Uch. zapiski EGU, 2008, no. 3, 16–24 | Zbl

[12] Karapetyan G. A., Darbinyan A. A., “Neterovost regulyarnogo operatora s postoyannymi koeffitsientami v oblasti”, Tr. Inst. Matematiki im. Razmadze, Tbilisi, 146, 2008, 57–66 | Zbl

[13] Karapetyan G. A., Petrosyan G. A., “Korrektnaya razreshimost zadachi Dirikhle v poluprostranstve dlya regulyarnykh uravnenii”, Izv. NAN Armenii. Mat., 53:4 (2018), 46–65 | MR | Zbl

[14] Karapetyan G. A., Petrosyan G. A., “Multianizotropnye integralnye operatory, opredelyaemye regulyarnymi uravneniyami”, Sib. matem. zhurn., 60:3 (2019), 610–629 | MR | Zbl

[15] Karapetyan G. A., Petrosyan G. A., “O razreshimosti regulyarnykh gipoellipticheskikh uravnenii v $\mathbb{R}^n$”, Izv. NAN Armenii. Mat., 54:4 (2019), 45–69 | MR | Zbl

[16] Karapetyan G. A., Khachatryan M. A., “Predelnye teoremy vlozheniya dlya multianizotropnykh funktsionalnykh prostranstv”, Izv. NAN Armenii. Mat., 54:2 (2019), 54–64 | MR | Zbl

[17] Karapetyants N. K., Samko S. G., Uravneniya s involyutivnymi operatorami i ikh prilozheniya, Izd-vo Rost. un-ta, Rostov n/D., 1988 | MR

[18] Lizorkin P. I., “Obobschennoe liuvillevskoe differentsirovanie i funktsionalnye prostranstva $L_{p}^r(E^n)$. Teoremy vlozheniya”, Matem. sb., 60 (102):3 (1963), 325–353 | Zbl

[19] Lizorkin P. I., “Obobschennoe liuvillevskoe differentsirovanie i metod multiplikatorov v teorii vlozhenii klassov differentsiruemykh funktsii”, Tr. MIAN SSSR, 105, 1969, 89–167 | Zbl

[20] V. V. Peller, Operatory Gankelya i ikh prilozheniya, RKhD, Izhevsk, 2005

[21] Sobolev S. L., “Ob odnoi teoreme funktsionalnogo analiza”, Matem. sb., 4 (46):3-C (1938), 471–497

[22] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, 3-e izd., Izd. LGU, M., 1988 | MR

[23] I. Stein, Singulyarnye integraly i differetsialnye svoistva funktsii, Mir, M., 1973

[24] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974

[25] L. Aizenberg, E. Liflyand, “Hardy spaces in Reinhardt domains, and Hausdorff operators”, Illinois J. Math., 53:4 (2009), 1033–1049 | DOI | MR | Zbl

[26] L. Aizenberg, E. Liflyand, A. Vidras, “Hausdorff operators in Hardy spaces on Cartan type domains in $\mathbb{C}^n$”, Israel Math. Conf. Proc.: Complex analysis and dynamical systems VI, v. 2, Contemp. Math., 667, AMS, Providence, RI, 2016, 27–46 | DOI | MR | Zbl

[27] G. Brown, F. Móricz, “Multivariate Hausdorff operators on the spaces $L^p(\mathbb{R}^n)$”, J. Math. Anal. Appl., 271:2 (2002), 443–454 | DOI | MR | Zbl

[28] V. I. Burenkov, Sobolev Spaces on domains, Tauber, Stutgart, 1998 | MR

[29] J. Chen, D. Fan, S. Wang, “Hausdorff operators on Euclidean spaces”, Appl. Math. J. Chinese Univ. Ser. B (4), 28 (2013), 548–564 | DOI | MR | Zbl

[30] A. Connes, Noncommutative geometry, Academic Press, London–San Diego, 1994 | MR | Zbl

[31] Darbinyan A. A., Tumanyan A. G., “On apriori estimates and the Fredholm property of differential operators in anisotropic spaces”, J. Contemp. Math. Anal., 53:2 (2018), 61–70 | DOI | MR | Zbl

[32] Darbinyan A. A., Tumanyan A. G., “On index stability of Noetherian differential operators in anisotropic Sobolev spaces”, Eurasian Math. J., 10:1 (2019), 9–15 | DOI | MR | Zbl

[33] P. Galanopoulos, M. Papadimitrakis, “Hausdorff and quasi-Hausdorff matrices on spaces of analytic functions”, Canad. J. Math., 58 (2006), 548–579 | DOI | MR | Zbl

[34] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman spaces, Graduate Texts of Math., 199, Springer-Verlag, New York, 2000 | DOI | MR | Zbl

[35] S. Janson, T. H. Wolff, “Schatten classes and commutators of singular integral operators”, Ark. Mat., 20:2 (1982), 301–310 | DOI | MR | Zbl

[36] N. K. Karapetiants, S. G. Samko, “Multi-dimensional integral operators with homogeneous kernels”, Fract. Calc. Appl. Anal., 2 (1999), 67–96 | MR | Zbl

[37] N. K. Karapetiants, S. G. Samko, Equations with involutive operators, Birkhäuser, Boston, 2001 | MR | Zbl

[38] Karapetyan G. A., “Galiardo–Nirenberg general inequalities for multianisotropic spaces”, Trans. A. Razmadze Math. Inst., 142 (2005), 6–11 | MR

[39] Karapetyan G. A., “The smooth dependence on parameter of solutions of regular equations”, Trans. A. Razmadze Math. Inst., 137 (2005), 6–11 | MR

[40] Karapetyan G. A., “Integral representations of functions and embedding theorems for multianisotropic spaces on the plane with one anisotropy vertex”, J. Contemp. Math. Anal., 51:6 (2016), 269–281 | DOI | MR | Zbl

[41] Karapetyan G. A., “An integral representation and embedding theorems in the plane for multianisotropic spaces”, J. Contemp. Math. Anal., 52:6 (2017), 261–269 | DOI | MR

[42] Karapetyan G. A., “Integral representation of functions and embedding theorems for multianisotropic spaces in the three-dimensional case”, Eurasian Math. J., 7:2 (2016), 19–37 | MR | Zbl

[43] Karapetyan G. A., Petrosyan H. A., “Embedding theorems for multianisotropic spaces with two vertices of anisotropicity”, Proc. YSU. Phys. and Math. Sci., 51:1 (2017), 29–37 | DOI | MR | Zbl

[44] A. Karapetyants, E. Liflyand, “Defining Hausdorff operators on Euclidean spaces”, Math. Meth. Appl. Sci., 43:16 (2020), 9487–9498 | DOI | MR | Zbl

[45] A. Karapetyants, S. Samko, K. Zhu, “A class of Hausdorff–Berezin operators on the unit disc”, Complex Anal. Oper. Theory, 13 (2019), 3853–3870 | DOI | MR | Zbl

[46] H. B. Lawson, M.-L. Michelsohn, Spin geometry, Math. Series, 38, Princeton Univ. Press, Princeton, NJ, 1989 | MR | Zbl

[47] A. Lerner, E. Liflyand, “Multidimensional Hausdorff operators on the real Hardy space”, J. Aust. Math. Soc., 83:1 (2007), 79–86 | DOI | MR | Zbl

[48] E. Liflyand, “Hausdorff operators on Hardy spaces”, Eurasian Math. J., 4:4 (2013), 101–141 | MR | Zbl

[49] E. Liflyand, F. Móricz, “The Hausdorff operator is bounded on the real Hardy space $H^{1}({\mathbb{R}})$”, Proc. Amer. Math. Soc., 128:5 (2000), 1391–1396 | DOI | MR | Zbl

[50] E. Liflyand, “Boundedness of multidimensional Hausdorff operators on $H^1(\mathbb{R}^n)$”, Acta Sci. Math. (Szeged), 74:3-4 (2008), 845–851 | MR | Zbl

[51] E. Liflyand, A. Miyachi, “Boundedness of the Hausdorff operators in $H^p$ spaces, $0

1$”, Studia Math., 194:3 (2009), 279–292 | DOI | MR | Zbl

[52] Tumanyan A. G., “On the invariance of index of semielliptical operator on the scale of anisotropic spaces”, J. Contemp. Math. Anal., 51:4 (2016), 167–178 | DOI | MR

[53] Tumanyan A. G., “Fredholm criteria for a class of regular hypoelliptic operators in multianisotropic spaces”, Italian J. Pure Appl. Math. (to appear)

[54] K. Zhu, Spaces of holomorphic functions in the unit ball, Graduate Texts of Math., 226, Springer Verlag, New York, 2005 | MR | Zbl

[55] K. Zhu, Operator theory in function spaces, Mathematical Surveys and Monographs, 138, AMS, Providence, RI, 2007 | DOI | MR | Zbl