Bloch范数的最大轨迹

Q3 Mathematics

Moroccan Journal of Pure and Applied Analysis Pub Date : 2023-05-01 DOI:10.2478/mjpaa-2023-0019

Youssfi El Hassan

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引用次数: 0

摘要

摘要:对于一个Bloch函数f在单位球上，研究了f的Bloch范数的极大轨迹;即f的梯度向量场的Bergman长度达到最大值的集合f。证明了当n≥时，集合Lf由维数不超过2n−2的实解析集的有限并构成。这与Cima和Wogen之前证明的n = 1的情况不同。我们也给出了集合Lf的一些刚性性质。特别地，我们给出了在小Bloch球上构造极值函数的几个充分的判据。

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The Maximum Locus of the Bloch Norm

Abstract For a Bloch function f in the unit ball in ℂn, we study the maximal locus of the Bloch norm of f; namely, the set Lf where the Bergman length of the gradient vector field of f attains its maximum. We prove that for n ≥, the set Lf consists of a finite union of real analytic sets with dimensions at most 2n − 2. This is not the case for n = 1 as was proved earlier by Cima and Wogen. We also give some rigidity properties of the set Lf. In particular, we give some sufficient criteria for constructing extreme functions in the Little Bloch ball.

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来源期刊

Moroccan Journal of Pure and Applied Analysis Mathematics-Numerical Analysis

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

8 weeks