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VOLUME INTEGRAL MEANS OF HARMONIC FUNCTIONS ON SMOOTH BOUNDARY DOMAINS
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 Title & Authors
VOLUME INTEGRAL MEANS OF HARMONIC FUNCTIONS ON SMOOTH BOUNDARY DOMAINS
Nam, Kyesook; Park, Inyoung;
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 Abstract
We newly define the volume integral means of harmonic functions to characterize the weighted harmonic Bergman spaces. It is based on Xiao and Zhu`s results on holomorphic Bergman spaces [5].
 Keywords
volume mean integral;harmonic Bergman spaces;smooth boundary domains in ;
 Language
English
 Cited by
 References
1.
S. Axler, P. Bourdon, and W. Ramey, Harmonic Function Theory, 2nd ed., Springer-Verlag, New York, 2001.

2.
S. G. Krantz and H. R. Parks, The Geometry of Domains in Space, Birkhauser Adv. Texts Basler Lehrbucher, Birkhauser Boston, Inc., Boston, Mass., 1999.

3.
K. Nam, Mean value property and a Berezin-type transform on the half-space, J. Math. Anal. Appl. 381 (2011), no. 2, 914-921. crossref(new window)

4.
M. Pavlovic, Hardy-Stein type characterization of harmonic Bergman spaces, Potential Anal. 32 (2010), no. 1, 1-15. crossref(new window)

5.
J. Xiao and K. Zhu, Volume integral means of holomorphic functions, Proc. Amer. Math. Soc. 139 (2011), no. 4, 1455-1465. crossref(new window)