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 ∂ △ belonging to Sobolev class H3/2.
关键词
渐近方差/调和Beltrami微分/Weil-Petersson类
Key words
asymptotic variance/harmonic Beltrami differential/Weil-Petersson class
维普
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