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The growth of H-harmonic functions on the Heisenberg group |
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| Authors: | HaiRong Liu Long Tian XiaoPing Yang |
| Affiliation: | 1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China 2. School of Science, Nanjing Forestry University, Nanjing, 210037, China |
| Abstract: | We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group. Precisely, we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded. Moreover, we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant. |
| Keywords: | Heisenberg group H-harmonic function frequency |
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