[1] Aizenberg L.Multidimensional analogues of Bohr’s theorem on power series. Proc Amer Math Soc, 2000, 128: 1147-1155
[2] Aizenberg L.Generalization of Caratheodory’s inequality and the Bohr radius for multidimensional power series. Advances and Applications, 2005, 158: 87-94
[3] Ali R M, Barnard R W, Solynin A Yu.A note on the Bohr’s phenomenon for power series. J Math Anal Appl, 2017, 449(1): 154-167
[4] Bayart F, Pellegrino D, Seoane-Sepúlveda J B. The Bohr radius of the n-dimensional polydisk is equivalent to p (log n)/n. Adv Math, 2014, 264: 726-746
[5] Bénéteau C, Dahlner A, Khavinson D.Remarks on the Bohr phenomenon. Comput Methods Funct Theory, 2004, 4(1): 1-19
[6] Bhowmik B, Das N.A note on the Bohr inequality. 2019, arXiv:1911.06597v1
[7] Boas H P, Khavinson D.Bohr’s power series theorem in several variables. Proc Amer Math Soc, 1997, 125: 2975-2979
[8] Bohr H.A theorem concerning power series. Proc Lond Math Soc, 1914, 2(13): 1-5
[9] Blasco O.The Bohr radius of a Banach space. Adv Appl Soc, 2009, 201: 59-64
[10] Bombieri E.Sopra un teorema di H. Bohr e G. Ricci sulle funzioni maggioranti delle serie di potenze. Boll Unione Mat Ital, 1962, 17: 276-282
[11] Bombieri E and Bourgain J. A remark on Bohr’s inequality. International Mathematics Research Notices, 2004, 80: 4307-4330
[12] Defant A, Frerick L.A logarithmic lower bound for multi-dimensional bohr radii. Israel J Math, 2006, 152(1): 17-28
[13] Defant A, Frerick L, Ortega-Cerdà J, Ounaïes M, Seip K.The Bohnenblust-Hille inequality for homogenous polynomials is hypercontractive. Ann of Math, 2011, 174(2): 512-517
[14] Defant A, Garca D, Maestre M, Sevilla-Peris P.Dirichlet Series and Holomorphic Functions in Higher Dimensions. New Mathematical Monographs, 37. Cambridge: Cambridge University Press, 2019
[15] Defant A, Prengel C.Christopher Harald Bohr meets Stefan Banach. Methods in Banach space theory// London Math Soc Lecture Note Ser, 337. Cambridge: Cambridge University Press, 2006: 317-339
[16] Dixon P G.Banach algebras satisfying the non-unital von Neumann inequality. Bull London Math Soc, 1995, 27(4): 359-362
[17] Djakov P B, Ramanujan M S.A remark on Bohr’s theorems and its generalizations. J Anal, 2000, 8: 65-77
[18] Garcia S R, Mashreghi J, Ross W T.Finite Blaschke Products and Their Connections. Cham: Springer, 2018
[19] Graham I, Kohr G.Geometric Function Theory in One and Higher Dimensions. New York: Marcel Dekker, 2003
[20] Hamada H, Honda T, Kohr G.Bohr’s theorem for holomorphic mappings with values in homogeneous balls. Israel J Math, 2009, 173: 177-187
[21] Kayumov I R, Ponnusamy S. Bohr-Rogosinski radius for analytic functions.2017, arXiv:1708.05585v1
[22] Kayumov I R, Ponnusamy S.Bohr’s inequality for analytic functions with Lacunary series and harmonic functions. J Math Anal Appl, 2018, 465(2): 857-871
[23] Kayumov I R, Ponnusamy S.On a powered Bohr inequality. Ann Acad Sci Fenn Ser A I Math, 2019, 44: 301-310
[24] Lin R Y, Liu M S, Ponnusamy S.Generalization of Bohr-type inequality in analytic functions. Acta Math Sin (Chin Ser), to appear in 2023, 65(1): 1-20. arXiv:2106.11158v1
[25] Liu M S, Wu F, Yang Y.Sharp estimates of quasi-convex mappings of type B and order alpha. Acta Mathematica Scientia, 2019, 39B(5): 1265-1276
[26] Liu M S, Shang Y M, Xu J F. Bhor-type inequalities of analytic functions. J Inequal Appl, 2018, 13: Art 345
[27] Liu M S, Ponnusamy S.Multidimensional analogues of refined Bohr’s inequality. Proc Amer Math Soc, 2021, 149(5): 2133-2146
[28] Liu X S. Sharp distortion theorems for a class of biholomorphic mappings in several complex variables. Acta Mathematica Scientia, 2022, 42 B(2): 454-466
[29] Liu X S, Liu T S. The Bohr’s inequality for holomorphic mappings with lacunary series in several complex variables. J Math Anal Appl, 2020, 485(2): Art 123844
[30] Liu T S, Wang J F.An absolute estimate of the homogeneous expansions of holomorphic mappings. Pacific J Math, 2007, 231: 155-166
[31] Paulsen V I, Popascu G, Singh D.On Bohr’s inequality. Proc Lond Math, 2002, 3(85): 493-512
[32] Paulsen V I, Singh D.Bohr’s inequality for uniform algebras. Proc Amer Math Soc, 2004, 132: 3577-3579
[33] Paulsen V I, Singh D.Extensions of Bohr’s inequality. Bull Lond Math Soc, 2006, 38(6): 991-999
[34] Ponnusamy S, Vijayakumar R, Wirths K-J. New inequalities for the coefficients of unimodular bounded functions. Results Math, 2020, 75: Art 107
[35] Ponnusamy S, Vijayakumar R, Wirths K J.Modifications of Bohr’s inequality in various settings. Houston J Math, 2021, to appear. arXiv:2104.05920v1
[36] Rogosinski W.On the coefficients of subordinate functions. Proc London Math Soc, 1943, 48(2): 48-82
[37] Sidon S.Uber einen satz von Herrn Bohr. Math Z, 1927, 26(1): 731-732
[38] Tomic M.Sur un theoreme de H. Bohr Math Scand, 1962, 11: 103-106
[39] Xu Q H, Fang F, Liu T S.On the Fekete and Szego problem for starlike mappings of orderα. Acta Math Sin (Engl Ser), 2017, 33: 554-564
[40] Xu Q H, Xu X. On the coefficient inequality for a subclass of strongly starlike mappings of order alpha in several complex variables. Results in Mathematics, 2018, 73: Art 73 |