准共形符号与投影复合算子
Quasiconformal symbols and projected composition operators
AI总结：
本文研究了在加权伯格曼空间上具有准共形符号的投影复合算子的可逆性，探讨了符号在不同区域内的共形性质及加权类别的影响。
摘要：
我们研究了在开放单位圆盘D上的加权伯格曼空间上，具有准共形符号g的投影复合算子K_g。如果符号是共形的，即D的莫比乌斯变换，则对应的复合算子至少在标准加权空间中自动可逆。我们证明，当Beltrami系数足够小时，可逆性仍然成立，特别是它在圆盘边界处满足某种消失条件。我们还考虑了符号g在环形区域{R < |z| < 1}内共形时K_g的可逆性。我们在考虑中的加权类别包括标准加权和指数递减加权。
英文摘要：
We study projected composition operators K_g with quasiconformal symbols g on weighted Bergman spaces on the open unit disc D. If the symbol were conformal, i.e.a Möbius transform of D, the corresponding composition operator would be automatically invertible at least in standard weighted spaces. We show that the invertibility remains, if the Beltrami coefficient is small enough, in particular, it satisfies a certain vanishing condition at the boundary of the disc. We also consider the invertibility of K_g for symbols g which are conformal in an annulus { R < |z| < 1 }. The weight classes in our considerations include both standard and exponentially decreasing weights.
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