Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 2039-2054.doi: 10.1007/s10473-021-0615-1
• Articles • Previous Articles Next Articles
Guanlong BAO, Hasi WULAN
Received:
2021-03-11
Revised:
2021-07-12
Online:
2021-12-25
Published:
2021-12-27
Supported by:
CLC Number:
Guanlong BAO, Hasi WULAN. $Q_K$ SPACES: A BRIEF AND SELECTIVE SURVEY[J].Acta mathematica scientia,Series B, 2021, 41(6): 2039-2054.
[1] | Wulan H, Zhu K. Möbius Invariant QK Spaces. Berlin:Springer-Verlag, 2017 |
[2] | Aulaskari R, Xiao J, Zhao R. On subspaces and subsets of BMOA and UBC. Analysis, 1995, 15(2):101-121 |
[3] | Xiao J. Holomorphic Q Classes. Lecture Notes in Mathematics 1767. Berlin:Springer-Verlag, 2001 |
[4] | Xiao J. Geometric Qp Functions. Basel, Boston, Berlin:Birkhäuser Verlag, 2006 |
[5] | Essén M, Wulan H. On analytic and meromorphic functions and spaces of QK type. Uppsala University, Department of mathematics Report, 2000:1-26. Illinois J Math, 2002, 46(4):1233-1258 |
[6] | Wu P, Wulan H. Characterizations of QT spaces. J Math Anal Appl, 2001, 254(2):484-497 |
[7] | Axler S. The Bergman spaces, the Bloch space, and commutators of multiplication operators. Duke Math J, 1986, 53(2):315-332 |
[8] | Baernstein II A. Analytic functions of bounded mean oscillation//Aspects of Contemporary Complex Analysis. London:Academic Press, 1980:3-36 |
[9] | Aulaskari R, Lappan P. Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal//Complex Analysis and Its Applications. Pitman Research Notes in Mathematics, 305. Harlow:Longman Scientific & Technical, 1994:136-146 |
[10] | Bao G, Mashreghi J, Pouliasis S, Wulan H. Möbius invariant function spaces and Dirichlet spaces with superharmonic weights. J Aust Math Soc, 2019, 106(1):1-18 |
[11] | Wulan H, Zhu K. Derivative free characterizations of QK spaces. J Aust Math Soc, 2007, 82(2):283-295 |
[12] | Zhou J, Han J. Interpolating sequences in QK spaces. J of Math (PRC), 2016, 36(3):511-518 |
[13] | Aleman A, Simbotin A. Estimates in Möbius invariant spaces of analytic functions. Complex Var Theory Appl, 2004, 49:487-510 |
[14] | Essén M, Wulan H, Xiao J. Function-theoretic aspects of Möbius invariant QK spaces. J Funct Anal, 2006, 230(1):78-115 |
[15] | Wulan H, Ye F. Universal Teichmüller space and QK spaces. Ann Acad Sci Fenn Math, 2014, 39(2):691-709 |
[16] | Wulan H, Zhu K. QK spaces via higher order derivatives. Rocky Mountain J Math, 2008, 38(1):329-350 |
[17] | Wulan H, Zhou J. QK and Morrey type spaces. Ann Acad Sci Fenn Math, 2013, 38(1):193-207 |
[18] | Wu Z, Xie C. Decomposition theorems for Qp spaces. Ark Mat, 2002, 40(2):383-401 |
[19] | Wulan H, Zhou J. Decomposition theorems for QK spaces and applications. Forum Math, 2014, 26(2):467-495 |
[20] | Rochberg R. Decomposition theorems for Bergman space and their applications in operators and function theory. Operator and Function Theory (Lancaster), NATO ASI Series C, 1984:225-277 |
[21] | Rochberg R, Semmes S. A decomposition theorem for BMO and applications. J Funct Anal, 1986, 67(2):228-263 |
[22] | Rochberg R, Wu Z. A new characterization of Dirichlet type spaces and applications. Illinois J. Math, 1993, 37(1):101-122 |
[23] | Stegenga D. Multipliers of the Dirichlet space. Illinois J Math, 1980, 24:113-139 |
[24] | Pau J, Peláez J. Multipliers of Möbius invariant Qs spaces. Math Z, 2009, 261(3):545-555 |
[25] | Li D, Wulan H. Corona and Wolff theorems for the multiplier algebras of QK spaces (in Chinese). Sci Sin Math, 2021, 51:301-314 |
[26] | Dyakonov K. Self-improving behaviour of inner functions as multipliers. J Funct Anal, 2006, 240(2):429- 444 |
[27] | Peláez J. Inner functions as improving multipliers. J Funct Anal, 2008, 255(6):1403-1418 |
[28] | Bao G, Lou Z, Qian R, Wulan H. Improving multipliers and zero sets in QK spaces. Collect Math, 2015, 66(3):453-468 |
[29] | Wulan H, Ye F. Some results in Möbius invariant QK spaces. Complex Var Elliptic Equ, 2015, 60(11):1602-1611 |
[30] | Li S, Wulan H. Derivative free characterizations of QK spaces II. Sarajevo J Math, 2006, 14(1):63-71 |
[31] | Bao G, Lou Z, Qian R, Wulan H. On absolute values of QK functions. Bull Korean Math Soc, 2016, 53(2):561-568 |
[32] | Ahlfors L. Lectures on Quasi-conformal Mappings. Princeton:Van Nostrand, 1966 |
[33] | Ahlfors L, Bers L. Riemann's mapping theorem for variable metrics. Ann Math, 1960, 72:385-404 |
[34] | Gehring F. Univalent functions and the Schwarzian derivative. Comment Math Helv, 1977, 52:561-572 |
[35] | Astala K, Gehring F. Injectivity, the BMO norm, and the universal Teichmüller space. J Anal Math, 1986, 46:16-57 |
[36] | Lehto O. Univalent Functions and Teichmüller Spaces. Springer-Verlag, 1987 |
[37] | Astala K, Zinsmeister M. Teichmüller spaces and BMOA. Math Ann, 1991, 289(4):613-625 |
[38] | Shen Y, Wei H. Universal Teichmüller space and BMO. Adv Math, 1999, 234:129-148 |
[39] | Wei H, Shen Y. On the tangent space to the BMO-Teichmüller space. J Math Anal Appl, 2014, 419(2):715-726 |
[40] | Jin J, Tang S. On QK-Teichmüller spaces. J Math Anal Appl, 2018, 467(1):622-637 |
[41] | Pommerenke Ch. On the mean growth of the solutions of complex linear differential equations in the disk. Complex Variables Theory Appl, 1982, 1(1):23-38 |
[42] | Li H, Li S. Nonlinear differential equation and analytic function spaces. Complex Var Elliptic Equ, 2018, 63(1):136-149 |
[43] | Li H, Wulan H. Linear differential equations with solutions in the QK spaces. J Math Anal Appl, 2011, 375(2):478-489 |
[44] | Shapiro J. The essential norm of a composition operator. Ann Math, 1987, 125:375-404 |
[45] | Shapiro J. Composition Operators and Classical Function Theory. New York:Springer-Verlag, 1993 |
[46] | De Branges L. A proof of the Bieberbach conjecture. Acta Math, 1985, 154:137-152 |
[47] | De Branges L. Underlying concepts in the proof of the Bieberbach conjecture. Proceedings of the International Congress of Mathematicians (Berkeley), 1986:25-42 |
[48] | Smith W, Zhao R. Composition operators mapping into the Qp spaces. Analysis, 1997, 17:239-263 |
[49] | Wu Y, Wulan H. Products of differentiation and composition operators on the Bloch space. Collect Math, 2012, 63(1):93-107 |
[50] | Bourdon P, Cima J, Matheson A. Compact composition operators on BMOA. Trans Amer Math Soc, 1999, 351(6):2183-2196 |
[51] | Smith W. Compactness of composition operators on BMOA. Proc Amer Math Soc, 1999, 127(9):2715-2725 |
[52] | Wulan H. Compactness of composition operators on BMOA and VMOA. Sci China Ser A, 2007, 50(7):997-1004 |
[53] | Wulan H, Zheng D, Zhu K. Compact composition operators on the Bloch and BMOA spaces. Proc Amer Math Soc, 2009, 137(11):3861-3868 |
[54] | Zhou J. Predual of QK spaces. J Funct Spaces Appl, 2013, 2013:Article ID 252735, 6 pages |
[55] | Zhan M, Cao G. Duality of QK-type spaces. Bull Korean Math Soc, 2014, 51(5):1411-1423 |
[56] | Perfekt K. Duality and distance formulas in spaces defined by means of oscillation. Ark Mat, 2013, 51(2):345-361 |
[57] | Korenblum B. BMO Estimates and radial growth of Bloch functions. Bull of Amer Math Soc (New Series), 1985, 12(1):99-102 |
[58] | Anderson J, Clunie J, Pommerenke Ch. On Bloch functions and normal functions. J Reine Angew Math, 1974, 270:12-37 |
[59] | Anderson J. Bloch functions:The basic theory//Power S C, ed. Operators and Function Theory, 152. Bordrecht:Reidel, 1984:1-17 |
[60] | Ghatage P, Zheng D. Analytic functions of bounded mean oscillation and the Bloch space. Int Equ Oper Theory, 1993, 17(4):501-515 |
[61] | Axler S, Zhu K. Boundary behavior of derivatives of analytic function. Michigan Math J, 1992, 39(1):129-143 |
[62] | Lou Z, Chen W. Distances from Bloch functions to QK type spaces. Integr Equ Oper Theory, 2010, 67(2):171-181 |
[63] | Zhao R. Distances from Bloch functions to some Möbius invariant spaces. Ann Acad Sci Fenn Math, 2008, 33(1):303-313 |
[64] | Galán N, Nicolau A. The closure of the Hardy space in the Bloch space norm. St Petersburg Math J, 2011, 22(1):55-59 |
[65] | Galanopoulos P, Galán N, Pau J. Closure of Hardy spaces in the Bloch space. J Math Anal Appl, 2015, 429(2):1214-1221 |
[66] | Tjani M. Distance of a Bloch function to the little Bloch space. Bull Aust Math Soc, 2006, 74(1):101-119 |
[67] | Danikas N, Siskakis A G. The Cesáro operator on bounded analytic functions. Analysis, 1993, 13(3):295-299 |
[68] | Essén M, Xiao J. Some results on Qp spaces, 0 |
[69] | Bao G, Wulan H, Ye F. The range of the Cesáro operator acting on H∞. Canad Math Bull, 2020, 63(3):633-642 |
[70] | Pau J, Peláez J. On the zeros of functions in Dirichlet-type spaces. Trans Amer Math Soc, 2011, 363(4):1981-2002 |
[71] | Fefferman C. Characterizations of bounded mean oscillations. Bull Amer Math Soc, 1971, 77:587-588 |
[72] | Fefferman C, Stein E. Hp spaces of several variables. Acta Math, 1972, 129:137-193 |
[73] | Nicolau A, Xiao J. Bounded functions in Möbius invariant Dirichlet spaces. J Funct Anal, 1997, 150(2):383-425 |
[74] | Pau J. Bounded Möbius invariant QK spaces. J Math Anal Appl, 2008, 338(2):1029-1042 |
[75] | Garnett J. Bounded Analytic Functions. New York:Academic Press, 1982 |
[76] | Jones P. L∞ estimates for the $\overline \partial $-problem in a half plane. Acta Math, 1983, 150:137-152 |
[77] | Carleson L. An interpolation problem for bounded analytic functions. Amer J Math, 1958, 80:921-930 |
[78] | Carleson L. Interpolations by bounded analytic functions and the corona problem. Ann Math, 1962, 76:547-559 |
[79] | Pau J. Multipliers of Qs spaces and the corona theorem. Bull Lond Math Soc, 2008, 40(2):327-336 |
[80] | Garnett J, Jones P. BMO from dyadic BMO. Pacific J Math, 1982, 99:351-371 |
[81] | Janson S. On the space Qp and its dyadic counterpart. Complex Analysis and Differential Equations (Uppsala), 1997:194-205 |
[82] | Essén M, Janson S, Peng L, Xiao J. Q-spaces of several real variables. Indiana Univ Math J, 2000, 49(2):575-615 |
[83] | Bao G, Wulan H. QK spaces of several real variables. Abstr Appl Anal, 2014:Art. ID 931937, 14 pp |
[84] | Bao G, Wulan H. John-Nirenberg type inequality and wavelet characterization for QK(Rn) spaces (in Chinese). Sci Sin Math, 2015, 45(11):1833-1846 |
[85] | Xu W. QK spaces on the unit ball of Cn. J Nanjing Norm Univ Nat Sc Ed, 2005, 28:21-28 |
[86] | Chen H, Xu W. Lacunary series and QK spaces on the unit ball. Ann Acad Sci Fenn Math, 2010, 35:47-57 |
[1] | Ruhan ZHAO. ON F(p,q,s) SPACES [J]. Acta mathematica scientia,Series B, 2021, 41(6): 1985-2020. |
|