Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1339-1344.doi: 10.1007/s10473-019-0512-z

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A SCHWARZ LEMMA FOR HARMONIC FUNCTIONS IN THE REAL UNIT BALL

Shaoyu DAI1, Huaihui CHEN2   

  1. 1. School of Mathematics, Southeast University, Nanjing 210096, China Department of Mathematics, Jinling Institute of Technology, Nanjing 211169, China;
    2. Department of Mathematics, Nanjing Normal University, Nanjing 210097, China
  • Received:2018-01-02 Revised:2018-12-21 Online:2019-10-25 Published:2019-11-11
  • Contact: Shaoyu DAI E-mail:dymdsy@163.com
  • Supported by:
    Research supported by the National Natural Science Foundation of China (11201199; 11071083; 11671361) and Jiangsu Overseas Visiting Scholar Program for University Prominent Young & Middle-aged Teachers and Presidents.

Abstract: We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.

Key words: harmonic functions, Schwarz-Pick lemma, unit ball

CLC Number: 

  • 31B05
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