共查询到20条相似文献,搜索用时 15 毫秒
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Ch. Pommerenke 《Mathematische Annalen》1978,236(3):199-208
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Carleson measure characterization of Bloch functions 总被引:1,自引:0,他引:1
Lou Zengjian 《数学学报(英文版)》1996,12(2):175-184
We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D
f(z)|
p
(1-|z|2)p-1
dm(z) is a generalized Carleson measure;f B
0 if and only if |D
f(z)|
p
(1-|z|2)p-1
dm(z) is a generalized vanishing Carleson measure, whereD
f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province. 相似文献
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E. S. Dubtsov 《Journal of Mathematical Sciences》2008,148(6):841-845
Let u be a strictly positive, harmonic Bloch function on the upper half-space ℝ
+
d+1
. Then the set
has the maximal Hausdorff dimension. Bibliography: 7 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 105–112. 相似文献
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S. Rohde 《Transactions of the American Mathematical Society》1996,348(7):2519-2531
We prove that analytic functions in the little Bloch space assume every value as a radial limit on a set of Hausdorff dimension one, unless they have radial limits on a set of positive measure. The analogue for inner functions in the little Bloch space is also proven, and characterizations of various classes of Bloch functions in terms of their level sets are given.
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A holomorphic functionf defined on the unit disk d is called a Bloch function provided {fx73-02} For α ∃ (0,1] letB∞(α)denote the class of locally univalent Bloch functionsf normalized by ∥f∥B ≤1f(0) = 0 andf’(0) = α. A type of subordination theorem is established for B∞(α). This subordination theorem is used to derive sharp growth,
distortion, curvature and covering theorems for B∞(α).
Supported as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation.
Research supported in part by a National Science Foundation grant. 相似文献
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Flavia Colonna 《Rendiconti del Circolo Matematico di Palermo》1989,38(2):161-180
Following a brief introduction to Bloch and normal functions, several conditions, including a convergence theorem, are shown for determining them. In addition, since an exponential of any constant multiple of a Bloch function is always normal, we investigate whether or not the converse holds, and construct an example of a non-Bloch function such that the exponential of any constant multiple of it is normal. 相似文献
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Journal d'Analyse Mathématique - 相似文献
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Evgueni Doubtsov 《Proceedings of the American Mathematical Society》2008,136(6):2177-2182
Let be an inner function in the unit ball , . Assume that where and is the radial derivative. Then, for all , the set has a non-zero real Hausdorff -content, and it has a non-zero complex Hausdorff -content.
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Daniel Girela Cristó bal Gonzá lez José Á ngel Pelá ez 《Proceedings of the American Mathematical Society》2006,134(5):1309-1314
A subspace of the Hardy space is said to have the -property if whenever and is an inner function with . We let denote the space of Bloch functions and the little Bloch space. Anderson proved in 1979 that the space does not have the -property. However, the question of whether or not ( ) has the -property was open. We prove that for every the space does not have the -property.
We also prove that if is any infinite Blaschke product with positive zeros and is a Bloch function with , as , then the product is not a Bloch function.
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An analogue of the universal integral means spectrum is definedfor Bloch functions, and is computed by using a suitable dyadicnorm. 相似文献
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Evgueni Doubtsov 《Archiv der Mathematik》2014,102(4):391-399
We show that N.G. Makarov’s law of the iterated logarithm governs the radial growth of weighted Bloch functions in the complex unit ball. The argument is based on an analog of M. Weiss’ theorem for special lacunary series in the ball. 相似文献
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We give a Fekete-Szeg? type inequality for an analytic function on the unit disk with Bloch seminorm ≤1. As an application
of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a
2
z
2 + a
3
z
3 + ⋯ on the unit disk with pre-Schwarzian norm ≤λ for a given λ > 0. 相似文献
20.
We give a Fekete-Szeg? type inequality for an analytic function on the unit disk with Bloch seminorm ≤1. As an application
of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a
2
z
2 + a
3
z
3 + ⋯ on the unit disk with pre-Schwarzian norm ≤λ for a given λ > 0.
The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B), 17340039.
Authors’ addresses: T. Sugawa and T. Terada, Department of Mathematics, Graduate School of Science, Hiroshima University,
Higashi-Hiroshima 739-8526, Japan
Current address: T. Sugawa, Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579,
Japan 相似文献