Acta mathematica scientia, Series B >
CARLESON MEASURES, RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p, q, s) SPACES IN THE UNIT BALL OF Cn
Received date: 2015-08-25
Revised date: 2015-11-28
Online published: 2016-06-25
Supported by
Supported in part by the National Natural Science Foundation of China (11271359) and the Fundamental Research Funds for the Central Universities (2014-Ia-037 and 2015-IVA-069).
This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F(p, q, s) spaces in the unit ball of Cn, which contain many classical function spaces, such as the Bloch space, BMOA and Qs spaces. The boundedness and compactness of these operators on F(p, q, s) spaces are characterized by means of an embedding theorem, i.e., F(p, q, s) spaces boundedly embedded into the tent-type spaces Tp,s∞(μ).
Ru PENG , You WU , Fangwen DENG . CARLESON MEASURES, RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p, q, s) SPACES IN THE UNIT BALL OF Cn[J]. Acta mathematica scientia, Series B, 2016 , 36(3) : 635 -654 . DOI: 10.1016/S0252-9602(16)30028-5
[1] Aleman A, Cima J. An integral operator on Hp and Hardy's inequality. J Anal Math, 2001, 85: 157-176
[2] Aleman A, Siskakis A G. An integral operator on Hp. Complex Variables, 1995, 28: 149-158
[3] Aleman A, Siskakis A G. Integral operators on Bergman spaces. Indiana Univ Math J, 1997, 46: 337-356
[4] Arcozzi N, Rochberg N, Sawyer E. Carleson measures for analytic Besov spaces. Rev Mat Iberoamericana, 2002, 18: 443-510
[5] Arcozzi N, Rochberg R, Sawyer E. Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls. Adv Math, 2008, 218: 1107-1180
[6] Aulaskari R, Xiao J, Zhao R. On subspaces and subsets of BMOA and UBC. Analysis, 1995, 15: 101-121
[7] Carleson L. Interpolation by bounded analytic functions and the corona problem. Ann Math, 1962, 76: 547-559
[8] Girela D, Peláez J A. Carleson measures, multipliers and integration operators for spaces of Dirichlet type. J Funct Anal, 2006, 241: 334-358
[9] Hu Z. Extended Cesáro operators on the Bloch space in the unit ball of Cn. Acta Math Sci, 2003, 23: 561-566
[10] Li B, Ouyang C. Higher radial derivative of functions of Qp spaces and its applications. J Math Anal Appl, 2007, 327: 1257-1272
[11] MacCluer B, Zhao R. Vanishing logarithmic Carleson measures. Illinois J Math, 2002, 46: 507-518
[12] Ohno S, Stroethoff K, Zhao R.Weighted composition operators between Bloch-type spaces. Rocky Mountain J Math, 2003, 33: 191-215
[13] Ortega J M, Fàbrega J. Corona type decomposition in some Besov spaces. Math Scand, 1996, 78: 93-111
[14] Ortega J M, Fàbrega J. Pointwise multipliers and corona type decomposition in BMOA. Ann Inst Fourier (Grenoble), 1996, 46: 111-137
[15] Ortega J M, Fàbrega J. Pointwise multipliers and decomposition theorems in Fs∞,q. Math Ann, 2004, 329: 247-277
[16] Ouyang C, Yang W, Zhao R. Mobius invariant Qp spaces associated with the Green's function on the unit ball of Cn. Pacific J Math, 1998, 182: 69-99
[17] Pau J, Zhao R. Carleson measures, Riemann-Stieltjes and multiplication operators on a general family of function spaces. Integral Equations and Operator Theory, 2014, 78: 483-514
[18] Pau J. Integration operators between Hardy spaces on the unit ball of Cn. http://arxiv.org/abs/1312.0727
[19] Peng R, Ouyang C. Riemann-Stieltjes operators and multipliers on Qp spaces in the unit ball of Cn. J Math Anal Appl, 2011, 377: 180-193
[20] Pommerenke C H. Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation. Comment Math Helv, 1977, 52: 591-602
[21] Rudin W. Function Theory in the Unit Ball of Cn. New York: Springer-Verlag, 1980
[22] Siskakis A G, Zhao R. A Volterra type operator on spaces of analytic functions//Function Spaces Contemp Math. Providence, RI: Amer Math Soc, 1999, 232: 299-311
[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. 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 London Math Soc, 2004, 70(2): 199-214
[27] Xiao J. The Qp Carleson measure problem. Adv Math, 2008, 217: 2075-2088
[28] Zhao R. On a general family of function spaces. Ann Acad Sci Fenn Math, Dissertations, 1996, 105: 56 pp
[29] Zhao R. On logarithmic Carleson measures. Acta Sci Math (Szeged), 2003, 69: 605-618
[30] Zhang X, Liu Y, Hu C. Several problems of F(p, q, s) space on the unit ball. J Nat Sci Hunan Norm Univ, 2009, 32: 3-6(in Chinese)
[31] Zhang X, He C, Cao F. The equivalent norms of F(p, q, s) space in Cn. J Math Anal Appl, 2013, 401: 601-610
[32] Zhu K. Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, 226. New York: Springer-Verlag, 2005
/
| 〈 |
|
〉 |