Grunsky算子的本性模

Essential Norm of the Grunsky Operator

利用一个推广的Grunsky不等式,借助于单叶函数的拟共形延拓的边界伸缩商,我们给出Grunsky算子的本性模的一些估计.作为推论,我们推出Grunsky算子的紧性准则.

By using a generalized Grunsky inequality, we obtain some estimates of the essential norm of the Grunsky operator for a univalent function in terms of the boundary distortion of the quasiconformal extension. As a corollary, we deduce the compactness criterion of the Grunsky operator.