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| On the Compactness of Grunsky Differential Operators |
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Citation： |
Li WU,Yuliang SHEN.On the Compactness of Grunsky Differential Operators[J].Chinese Annals of Mathematics B,2020,41(4):589~572 |
| Page view： 431
Net amount： 387 |
Authors： |
Li WU; Yuliang SHEN |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 11631010). |
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| Abstract： |
Grunsky operators play an important role in classical geometric function theory and in the study of Teichm¨uller spaces. The Grunsky map is known to be holomorphic on the universal Teichm¨uller space. In this paper the authors deal with the compactness of a Grunsky differential operator. They will give upper and lower estimates of the essential norm of a Grunsky differential operator and discuss when a Grunsky differential operator is a p-Schatten class operator. |
Keywords： |
Universal Teichm¨uller space, Beltrami coefficient, Grunsky operator, Compact operator, p-Schatten class operator, Essential norm |
Classification： |
30C62, 32G15 |
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