[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2014.51.4.1195

VOLUME INTEGRAL MEANS OF HARMONIC FUNCTIONS ON SMOOTH BOUNDARY DOMAINS

Nam, Kyesook (Department of Mathematics Seoul National University)
Park, Inyoung (The Center of GAIA Pohang University of Science and Technology)

Publication Information

Bulletin of the Korean Mathematical Society / v.51, no.4, 2014 , pp. 1195-1204 More about this Journal

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 $\mathbf{R}_n$ ;

Citations & Related Records

Reference

1	K. Nam, Mean value property and a Berezin-type transform on the half-space, J. Math. Anal. Appl. 381 (2011), no. 2, 914-921. DOI ScienceOn
2	M. Pavlovic, Hardy-Stein type characterization of harmonic Bergman spaces, Potential Anal. 32 (2010), no. 1, 1-15. DOI
3	J. Xiao and K. Zhu, Volume integral means of holomorphic functions, Proc. Amer. Math. Soc. 139 (2011), no. 4, 1455-1465. DOI ScienceOn
4	S. Axler, P. Bourdon, and W. Ramey, Harmonic Function Theory, 2nd ed., Springer-Verlag, New York, 2001.
5	S. G. Krantz and H. R. Parks, The Geometry of Domains in Space, Birkhauser Adv. Texts Basler Lehrbucher, Birkhauser Boston, Inc., Boston, Mass., 1999.