调和Bergman-Orlicz空间的Lipschitz型刻画
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摘要
本文研究了上半空间和单位球上的调和Bergman-Orlicz空间的刻画及调和函数差商的有界性.给出了调和Bergman-Orlicz空间分别在欧氏度量,双曲型度量,伪双曲型度量下的Lipschitz型刻画.利用这些刻画获得了调和函数差商的有界性,这些结果推广了相应于上半空间和单位球上的调和Bergman空间上的结果.
We study characterizations of harmonic Bergman-Orlicz spaces and the boundedness of difference quotients of harmonic functions on the upper half-space or the unit ball. First,we give Lipschitz type characterizations of harmonic Bergman-Orlicz spaces via the Euclidean,hyperbolic, and pseudo-hyperbolic metrics. By these characterizations, we obtain the boundedness of difference quotients of harmonic functions on the upper half-space or the unit ball, which generalize those for harmonic Bergman spaces on the upper half-space or the unit ball.
We study characterizations of harmonic Bergman-Orlicz spaces and the boundedness of difference quotients of harmonic functions on the upper half-space or the unit ball. First,we give Lipschitz type characterizations of harmonic Bergman-Orlicz spaces via the Euclidean,hyperbolic, and pseudo-hyperbolic metrics. By these characterizations, we obtain the boundedness of difference quotients of harmonic functions on the upper half-space or the unit ball, which generalize those for harmonic Bergman spaces on the upper half-space or the unit ball.
引文
[1] Wulan H, Zhu K. Lipschitz type characterizations for Bergman spaces[J]. Canad. Math. Bull., 2009,52(4):613–626.
[2] Nam K. Lipschitz type characterizations of harmonic Bergman spaces[J]. Bull. Korean Math. Soc.,2013, 50(4):1277–1288.
[3] Choe B R, Yi H. Representations and interpolations of harmonic Bergman functions on half spaces[J]. Nagoya Math. J., 1998, 151(39):51–89.
[4] Coifman R R, Rochberg R. Representation theorems for holomorphic and harmonic functions in L[J]. Aste′risque. 1980, 77:459–460.
[5] Pavlovic M, On subharmonic behavior and oscilation of functions on balls in Rn[J]. Publ. Inst.Math.(Beograd)(N.S.), 1994, 55(69):18–22.
[6] Axler S, Bourdon P, Ramey W. Harmonic function theory[M]. New York:Springer-Verlag, 1992.
[7] Choe B R, Nam K. Berezin transform and Toepliz operators on harmonic Bergman spaces[J]. J.Funct. Anal., 2009, 257(10):3135–3166.
[8] Hardy G H, Littlewood J E. Some properties of conjugate functions[J]. J. Reine Angew. Math.,1932, 1932(167):405–423.
[9] Pavlovic M. Hardy-Stein type characterization of harmonic Bergman spaces[J]. Potential Anal.,2010, 32(1):1–15.
[10] Choe B R, Koo H, Lee Y J. Positive Schatten class Toeplitz operators on the ball[J]. Studia Math.,2008, 189(1):65–90.
[2] Nam K. Lipschitz type characterizations of harmonic Bergman spaces[J]. Bull. Korean Math. Soc.,2013, 50(4):1277–1288.
[3] Choe B R, Yi H. Representations and interpolations of harmonic Bergman functions on half spaces[J]. Nagoya Math. J., 1998, 151(39):51–89.
[4] Coifman R R, Rochberg R. Representation theorems for holomorphic and harmonic functions in L[J]. Aste′risque. 1980, 77:459–460.
[5] Pavlovic M, On subharmonic behavior and oscilation of functions on balls in Rn[J]. Publ. Inst.Math.(Beograd)(N.S.), 1994, 55(69):18–22.
[6] Axler S, Bourdon P, Ramey W. Harmonic function theory[M]. New York:Springer-Verlag, 1992.
[7] Choe B R, Nam K. Berezin transform and Toepliz operators on harmonic Bergman spaces[J]. J.Funct. Anal., 2009, 257(10):3135–3166.
[8] Hardy G H, Littlewood J E. Some properties of conjugate functions[J]. J. Reine Angew. Math.,1932, 1932(167):405–423.
[9] Pavlovic M. Hardy-Stein type characterization of harmonic Bergman spaces[J]. Potential Anal.,2010, 32(1):1–15.
[10] Choe B R, Koo H, Lee Y J. Positive Schatten class Toeplitz operators on the ball[J]. Studia Math.,2008, 189(1):65–90.