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Harmonic Bergman functions as radial derivatives of Bergman functions

Author(s): Boo Rim Choe; Hyungwoon Koo; HeungSu Yi
Journal: Proc. Amer. Math. Soc. 131 (2003), 401-408.
MSC (2000): Primary 31B05, 31B10; Secondary 32A36
Posted: September 19, 2002
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Abstract: In the setting of the half-space of the euclidean -space, we show that every harmonic Bergman function is the radial derivative of a Bergman function with an appropriate norm bound.

References:

1.: H. Ajmi, Harmonic Bloch functions on the upper half-space, Ph.D. Thesis, Michigan State University, 1992.
2.: S. Axler, P. Bourdon and W. Ramey, Harmonic function theory, Springer-Verlag, New York, 1992. MR 93f:31001
3.: B. R. Choe, H. Koo, and H. Yi, Gleason's problem for harmonic Bergman and Bloch functions on half-spaces, Integr. Equ. Oper. Theory 36 (2000), 269-287. MR 2001c:46040
4.: B. R. Choe, and H. Yi, Representations and interpolations of harmonic Bergman functions on half-spaces, Nagoya Math. J. 151 (1998), 51-89. MR 99k:31002
5.: W. Ramey and H. Yi, Harmonic Bergman functions on half-spaces, Trans. Amer. Math. Soc. 348(1996), 633-660. MR 96g:31006

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Additional Information:

Boo Rim Choe
Affiliation: Department of Mathematics, Korea University, Seoul 136--701, Korea
Email: choebr@math.korea.ac.kr

Hyungwoon Koo
Affiliation: Department of Mathematics, Korea University, Seoul 136--701, Korea
Email: koohw@math.korea.ac.kr

HeungSu Yi
Affiliation: Department of Mathematics, Kwangwoon University, Seoul 139--701, Korea
Email: hsyi@gwu.ac.kr

DOI: 10.1090/S0002-9939-02-06531-0
PII: S 0002-9939(02)06531-0
Keywords: Bergman functions, radial derivative, upper half-space
Received by editor(s): April 18, 2001
Posted: September 19, 2002
Additional Notes: This study was supported in part by the Research Grant of Kwangwoon University in 2001, KOSEF 2000-1-10100-001-3 and KOSEF 98-0701-03-01-5
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2002, American Mathematical Society


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