On the mean growth of the solutions of complex linear differential equations in the disk
On the mean growth of the solutions of complex linear differential equations in the disk
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DOI：
10.1080/17476938208814004
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发表时间：
1982-09
影响因子：
0.9
通讯作者：
C. Pommerenke
中科院分区：
文献类型：
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作者：
C. Pommerenke
设w是微分方程w（z）+q（z）w（z）=0的解，其中q在单位圆盘内解析.首先研究了W的均方增长性，给出了W属于哈代空间H 2的条件：证明是基于Carleson测度的。然后证明了，暗示W具有有界特征：证明使用了Hille的思想和哈代Littlewood极大值定理。这个结果最后被应用到q是某个Fuchsian群的权为2的n-自守形式的情况，如果我们考虑多连通域中的微分方程，然后使用一致化，这种情况就会出现。
Let w be a solution of the differential equation w(z)+q(z)w(z)=0 where q is analytic in the unit disk. We study first the mean square growth of w and give a condition for w to belong to the Hardy space H2 : the proof is based on Carleson measures Then it is shown that implies that w is of bounded characteristic: the proof uses ideas of Hille together with the Hardy Littlewood maximal theorem. This result is finally applied to the case that q is a Г-automorphic form of weight 2 for some Fuchsian group Г this case arises if we consider our differential equation in a multiply connected domain and then use uniformization.