Acta mathematica scientia,Series A ›› 1997, Vol. 17 ›› Issue (1): 90-94.

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The Converse to the Mean Value Theorem for Harmonic Functions and Harmonic Measure

Liu Jiakun1, Lai Xuejian2   

  1. 1 Tianjin Univ.;
    2 Nankai Univ
  • Received:1995-03-16 Revised:1996-05-16 Online:1997-02-26 Published:1997-02-26

Abstract: In this paper we apply the theory of Markov chains to prove the converse to the mean value theorem for harmonic functions. And in a λ-Hölder space we derive convergent rate of n-fold convolution of averaging operator.

Key words: harmonic function, Markov chains, martingale, λ-Hölder space

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