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Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of Cn in terms of Lipschitz type condi- tions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in Rn. Further- more, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < 1. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.
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참고문헌 신청
B. R. Choe / 1998 / Representations and interpolations of harmonic Bergman functions on half spaces / Nagoya Math. J 151 : 51 ~ 89
B. R. Choe / 2008 / Positive Schatten class Toeplitz operators on the ball / Studia Math 189 (1) : 65 ~ 90
B. R. Choe / 2009 / Berezin transform and Toeplitz operators on harmonic Bergman spaces / J. Funct. Anal 257 (10) : 3135 ~ 3166
B. R. Choe / 2011 / Double integral characterizations of harmonic Bergman spaces / J. Math. Anal. Appl 379 (2) : 889 ~ 909
G. H. Hardy / 1932 / Some properties of conjugate functions / J. Reine Angew. Math 167 : 405 ~ 423
B. R. Choe / 2008 / Positive Schatten class Toeplitz operators on the ball / Studia Math 189 (1) : 65 ~ 90
B. R. Choe / 2009 / Berezin transform and Toeplitz operators on harmonic Bergman spaces / J. Funct. Anal 257 (10) : 3135 ~ 3166
B. R. Choe / 2011 / Double integral characterizations of harmonic Bergman spaces / J. Math. Anal. Appl 379 (2) : 889 ~ 909
G. H. Hardy / 1932 / Some properties of conjugate functions / J. Reine Angew. Math 167 : 405 ~ 423
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