积分平均形式和调和Beltrami微分

Abstract

Abstract: In this paper we investigate the relationship between the integral averages norms of some analytic functions and the harmonic Beltrami differentials induced by some holomorphic quadratic differentials. We discuss that under what conditions are the holomorphic forms with finite asymptotic variances. The paper offers a new criterion method for a harmonic Beltrami differential belonging to the Weil-Petersson class by the integral means norms. Furthermore we give a method of determining a homeomorphism $g$ of the unit circle $\partial\Delta$ belonging to Sobolev class $H^{\frac{3}{2}}$.

Key words: asymptotic variance, harmonic Beltrami differential, Weil-Petersson class

CLC Number:

O175

Huo Shengjin, Shao Wanting. Integral Averages forms and Harmonic Beltrami Differentials[J].Acta mathematica scientia,Series A, 2025, 45(1): 189-202.

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References

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Integral Averages forms and Harmonic Beltrami Differentials

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