Ru PENG
,
Xiaolei XING
,
Liangying JIANG
. POINTWISE MULTIPLICATION OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF Cn[J]. Acta mathematica scientia, Series B, 2019
, 39(4)
: 1003
-1016
.
DOI: 10.1007/s10473-019-0407-z
[1] Carleson L. An interpolation problem for bounded analytic functions. Amer J Math, 1958, 80:921-930
[2] Carleson L. Interpolations by bounded analytic functions and the corona problem. Ann of Math, 1962, 76:547-559
[3] Duren P. Extension of a theorem of Carleson. Bull Amer Math Soc, 1969, 75:143-146
[4] Feldman N S. Pointwise multipliers from the Hardy space to the Bergman space. Illinois J Math, 1999, 43:211-221
[5] Hörmander L. Lp estimates for (pluri-) subharmonic functions. Math Scand, 1967, 20:65-78
[6] Hu P Y, Shi J H. Multipliers on Dirichlet type spaces. Acta Math Sinica (Engl Ser), 2001, 17(2):263-272
[7] Hu Z J. Extended Cesáro operators on the Bloch space in the unit ball of Cn. Acta Mathematica Scientia, 2003, 23B:561-566
[8] Li B, Ouyang C H. Higher radial derivative of Bloch type functions. Acta Mathematica Scientia, 2002, 22B(4):433-445
[9] Li B, Ouyang C H. Higher radial derivative of functions of Qp spaces and its applications. J Math Anal Appl, 2007, 327:1257-1272
[10] Li S, Stevic S. Riemann-Stieltjes operators between different weighted Bergman spaces. Bull Belg Math Soc Simon Stevin, 2008, 15:677-686
[11] Luecking D H. Embedding derivatives of Hardy spaces into Lebesgue spaces. Proc Lond Math Soc, 1991, 63:595-619
[12] Ortega J M, Fàbrega J. Pointwise multipliers and corona type decomposition in BMOA. Ann Inst Fourier(Grenoble), 1996, 46:111-137
[13] Ortega J M, Fàbrega J. Pointwise multipliers and decomposition theorems in Fs∞,q. Math Ann, 2004, 329:247-277
[14] Ouyang C H, Yang W S, Zhao R H. Characterizations of Bergman spaces and Bloch space in the unit ball of Cn. Trans Amer Math Soc, 1995, 347:4301-4313
[15] Ouyang C H, Yang W S, Zhao R H. Mobius invariant Qp Spaces associated with the Green's function on the unit ball of Cn. Pacific J Math, 1998, 182:69-99
[16] Pau J, Zhao R H. Carleson measure, Riemann-Stieltjes and multiplication operators on a general family of function spaces. Integral Equations and Operator Theory, 2014, 78:483-514
[17] Pau J. Integration operators between Hardy spaces on the unit ball of Cn. J Funct Anal, 2016, 270:134-176
[18] Peng R, Ouyang C H. Pointwise multipliers from Dirichlet type spaces Dτ to Qp spaces in the unit ball of Cn. J Math Anal Appl, 2008, 338:1448-1457
[19] Peng R, Ouyang C H. Riemann-Stieltjes operators and multipliers on Qp spaces in the unit ball of Cn. J Math Anal Appl, 2011, 377:180-193
[20] Peng R, Wu Y, Deng F W. Carleson measures, Riemann-Stieltjes operators and multipliers on F(p, q, s) spaces in the unit ball of Cn. Acta Mathematica Scientia, 2016, 36B:635-654
[21] Pommerenke C H. Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation. Comment Math Helv, 1997, 52:591-602
[22] Rudin W. Function Theory in the Unit Ball of Cn. New York:Springer-Verlag, 1980
[23] Stegenga D A. Multipliers of the Dirichlet space. Illinois J Math, 1980, 24:113-139
[24] Tjani M. Compact composition operators on Besov spaces. Trans Amer Math Soc, 2003, 355:4683-4698
[25] Wu Z J. Carleson measures and multipliers for Dirichlet spaces. J Funct Anal, 1999, 169:148-163
[26] Xiao J. Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball. J Lond Math Soc, 2004, 70:199-214
[27] Xiao J. Riemann-Stieltjes integral operators between weighted Bergman spaces. Mathematics, 2006
[28] Xiao J. The Qp Carleson measure problem. Advances in Mathmatics, 2008, 217:2075-2088
[29] Yang W S. Carleson type measure characterization of Qp spaces. Analysis, 1998, 18:345-349
[30] Yang W S. Vanishing Carleson type measure characterization of Qp,0. C R Math Rep Acad Sci Canada, 1999, 21(1):1-5
[31] Zhang X J. The pointwise multipliers of Bloch type space βp and Dirichlet type space Dq on the unit ball of Cn. J Math Anal Appl, 2003, 285:376-386
[32] Zhang X, Xiao J, Hu Z, Liu Y, Xiong D, Wu Y. Equivalent characterization and application of F(p, q, s) space in Cn. Acta Mathematica Sinica, 2011, 54:1029-1042(in Chinese)
[33] Zhang X J, He C Z, Cao F F. The equivalent norms of F(p, q, s) space in Cn. J Math Anal Appl, 2013, 401:601-610
[34] Zhao R H. On a general family of function spaces. Ann Acad Sci Fenn Math Dissertations, 1996, 105:56
[35] Zhao R H. Pointwise multipliers from weighted Bergman spaces and Hardy spaces to weighted Bergman spaces. Annales Academiæ Scientiarum Fennicæ, 2004, 29:139-150
[36] Zhao R H, Zhu K H. Theory of Bergman Spaces in the unit ball of Cn. Mem Soc Math Fr, 2008, 115
[37] Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics. Vol 226. New York:Springer-Verlag, 2005