DOI QR코드

DOI QR Code

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)
  • Received : 2013.10.24
  • Published : 2014.07.31

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

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. https://doi.org/10.1016/j.jmaa.2011.04.015
  4. M. Pavlovic, Hardy-Stein type characterization of harmonic Bergman spaces, Potential Anal. 32 (2010), no. 1, 1-15. https://doi.org/10.1007/s11118-009-9140-x
  5. J. Xiao and K. Zhu, Volume integral means of holomorphic functions, Proc. Amer. Math. Soc. 139 (2011), no. 4, 1455-1465. https://doi.org/10.1090/S0002-9939-2010-10797-9