DOI QR코드

DOI QR Code

ON THE VOLUME MEAN VALUE PROPERTY FOR M-HARMONIC FUNCTIONS

  • Published : 2003.07.01

Abstract

We will show that if U is a Bergman ball E($\alpha;\;\delta$) in $B_n\;\subset\;{\mathbb{C}_n}$ and if U has M-harmonic volume mean value property at a for all M-harmonic functions f on $\={U} $, then U must be a ball centered at the origin with $\alpha\;=\;0$.

Keywords

References

  1. Journal of Functional Analysis v.111 An Invariant Volume-Mean-Value Property P.Ahern;M.Flores;W.Rudin https://doi.org/10.1006/jfan.1993.1018
  2. Complex Variables v.13 The Volume Mean-Value Property of Harmonic Functions D.H.Armigate;M.Goldstein https://doi.org/10.1080/17476939008814389
  3. Proc. Amer. Math. Soc. v.122 no.4 A Converse of the Volume-mean Value Property for Invariant Harmonic Functions J.Bruna;J.Detraz https://doi.org/10.2307/2161170
  4. Amer. Math. Soc. v.13 On The Mean Value Property of Harmonic Functions B.Epstein https://doi.org/10.2307/2034188
  5. Bull. London Math. Soc. v.4 On the mean-value property of harmonic functions U.Kuran https://doi.org/10.1112/blms/4.3.311
  6. Function Theory in the unit ball of $\mathbb{C}^ n$ Walter Rudin
  7. Real and Complex analysis Walter Rudin
  8. Invariant Potential Theory in The Unit Ball of $\mathbb{C}^ n$ M.Stoll