Acta mathematica scientia, Series B >
CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF Cn
Received date: 2012-08-22
Online published: 2013-09-20
Supported by
Supported in part by the National Natural Science Foundation of China (10971219, 11126048 and 11101279) and the Fundamental Research Funds for the Central Universities (2012-Ia-018).
This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bσp (B) and p-Carleson measure in the unit ball of Cn. As appli-cations, we characterize the Riemann-Stieltjes operators and multipliers acting on Bσp (B) spaces by means of Carleson measures for Bσp (B).
PENG Ru , OUYANG Cai-Heng . CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF Cn[J]. Acta mathematica scientia, Series B, 2013 , 33(5) : 1219 -1230 . DOI: 10.1016/S0252-9602(13)60075-2
[1] Arcozzi N, Rochberg R, Sawyer E. Carleson measures for analytic Besov spaces. Rev Mat Iberoamericana, 2002, 18: 443–510
[2] Arcozzi N, Rochberg R, Sawyer E. Carleson measures and interpolating sequences for Besov spaces on complex balls. Mem Amer Math Soc, 2006, 182: vi+163pp
[3] 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
[4] Carleson L. An interpolation problem for bounded analytic functions. Amer J Math, 1958, 80: 921–930
[5] Duren P L. Extension of a theorem of Carleson. Bull Amer Math Soc, 1969, 75: 143–146
[6] Girela D, Pel´aez J A. Carleson measures, multipliers and integration operators for spaces of Dirichlet type. J Funct Anal, 2006, 241: 334–358
[7] Hu Z J. Extended Ces´aro operators on the Bloch space in the unit ball of Cn. Acta Math Sci, 2003, 23: 561–566
[8] Kerman R, Sawyer E. Carleson measure and multipliers of Dirichlet type spaces. Trans Amer Math Soc, 1988, 309: 87–98
[9] Li S, Stevi´c S. Riemann-Stieltjes operators on Hardy spaces in the unit ball of Cn. Bull Belg Math Soc Simon Stevin, 2007, 14: 621–628
[10] Luecking D H. Forward and reverse inequalities for functions in Bergman spaces and their derivatives. Amer J Math, 1985, 107: 85–111
[11] Ortega J M, F`abrega J. Corona type decomposition in some Besov spaces. Math Scand, 1996, 78: 93-111
[12] Ortega J M, F`abrega J. Pointwise multipliers and corona type decomposition in BMOA. Ann Inst Fourier(Grenoble), 1996, 46: 111–137
[13] Ortega J M, F`abrega J. Pointwise multipliers and decomposition theorems in F∞,qs . 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] Peng R, Ouyang C H. Pointwise multipliers from Dirichlet type spaces D to Qp spaces in the unit ball
of Cn. J Math Anal Appl, 2008, 338: 1448–1457
[16] Rudin W. Function Theory in the Unit Ball of Cn. New York: Springer-Verlag, 1980
[17] Stegenga D A. Multipliers of the Dirichlet space. Illinois J Math, 1980, 24: 113–139
[18] Volberg A, Wick B D. Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball. Amer J Math, 2012, 134: 949–992
[19] Wu Z J. Carleson measures and multipliers for Dirichlet spaces. J Funct Anal, 1999, 169: 148–163
[20] Xiao J. Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball. J London Math Soc, 2004, 70(2): 199–214
[21] Xiao J. The Qp Carleson measure problem. Adv Math, 2008, 217: 2075–2088
[22] Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, Vol 226. New York: Springer-Verlag, 2005
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