Abstract:
This paper considers an extension of the class of holomorphic functions. Analogues of classical theorems on holomorphic functions are proved for functions in the wider class. As an application, generalizations of a number of properties of holomorphic functions are obtained.
Bibliography: 12 titles.
This publication is cited in the following 34 articles:
A. B. Sukhov, “On holomorphic mappings of strictly pseudoconvex domains”, Sb. Math., 213:11 (2022), 1597–1619
Ufa Math. J., 14:3 (2022), 127–140
Alexandre Sukhov, “On the Fatou theorem for ∂̄J-subsolutions in wedges”, Proceedings of the Edinburgh Mathematical Society, 65:3 (2022), 760
A. B. Sukhov, “Holomorphic mappings between domains with low boundary regularity”, Izv. Math., 85:3 (2021), 536–546
Hidetaka Hamada, Mihai Iancu, Gabriela Kohr, “Spiralshapelike mappings in several complex variables”, Annali di Matematica, 199:6 (2020), 2181
S. Pinchuk, R. Shafikov, A. Sukhov, “Some Aspects of Holomorphic Mappings: A Survey”, Proc. Steklov Inst. Math., 298 (2017), 212–247
Krantz S., “Harmonic and Complex Analysis in Several Variables”, Harmonic and Complex Analysis in Several Variables, Springer Monographs in Mathematics, Springer, 2017, 1–424
S. Berhanu, Ming Xiao, “On the regularity of CR mappings between CR manifolds of hypersurface type”, Trans. Amer. Math. Soc., 369:9 (2017), 6073
Hill C.D., Nacinovich M., “Non Completely Solvable Systems of Complex First Order PDE'S”, Rend. Semin. Mat. Univ. Padova, 129 (2013), 129–169
Bernard Coupet, Hervé Gaussier, Alexandre Sukhov, “Some aspects of analysis on almost complex manifolds with boundary”, Journal of Mathematical Sciences (New York), 154:6 (2008), 923
François Berteloot, “Méthodes de changement d'échelles en analyse complexe”, Annales de la Faculté des sciences de Toulouse : Mathématiques, 15:3 (2008), 427
Hervé Gaussier, Alexandre Sukhov, “On the geometry of model almost complex manifolds with boundary”, Math Z, 254:3 (2006), 567
Seshadri H. Verma K., “On Isometries of the Caratheodory and Kobayashi Metrics on Strongly Pseudoconvex Domains”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 5:3 (2006), 393–417
Bernard Coupet, Hervé Gaussier, Alexandre Sukhov, “Fefferman’s mapping theorem on almost complex manifolds in complex dimension two”, Math Z, 250:1 (2005), 59
Bernard Coupet, Alexandre Sukhov, “Reflection principle and boundary properties of holomorphic mappings”, Journal of Mathematical Sciences (New York), 125:6 (2005), 825
Tumanov A., “Extremal Discs and the Geometry of Cr Manifolds”, Real Methods in Complex and Cr Geometry, Lecture Notes in Mathematics, 1848, eds. Abate M., Fornaess J., Huang X., Rosay J., Tumanov A., Springer-Verlag Berlin, 2004, 191–212
Giuseppe Zampieri, “Reflection about k-jets and holomorphic extension of CR mappings”, Journal of Mathematical Analysis and Applications, 283:1 (2003), 150
Tumanov A., “Extremal Discs and the Regularity of Cr Mappings in Higher Codimension”, Am. J. Math., 123:3 (2001), 445–473
Balogh Z., Bonk M., “Gromov Hyperbolicity and the Kobayashi Metric on Strictly Pseudoconvex Domains”, Comment. Math. Helv., 75:3 (2000), 504–533