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Carleson measure characterization of Bloch functions   总被引:1,自引:0,他引:1  
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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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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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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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 ∥fB ≤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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Journal d'Analyse Mathématique -  相似文献   

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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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Bloch型函数关于径向导数的积分判据   总被引:12,自引:2,他引:10  
研究了Bloch型函数的径向导数,给出了α-Bloch(小α-Bloch)函数的几个关于径向导数的积分判据。  相似文献   

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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   

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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. 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   

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In this paper we show that the closure of the space BMOA of analytic functions of bounded mean oscillation in the Bloch spaceB is the image P(U) of space of all continuous functions on the maximal ideal space ofH under the Bergman projection P. It is proved that the radial growth of functions in P(U) is slower than the iterated logarithm studied by Makarov. So some geometric conditions are given for functions in P(U), which we can easily use to construct many Bloch functions not in P(U).  相似文献   

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We study the functions {B(rn(t))}, where B is a Banach limit and {rn(t)} are Rademacher functions.  相似文献   

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The densities of polynomial-normal distributions (PND) are the product of nonegative polynomials and normal densities. These densities provide a rich class of distributions that can be used in modeling when faced with nonnormal characteristics such as skewness and multimodality. We give necessary and sufficient conditions for φ to be a characteristic function (ch.f.) of a PND. Then we given an effective construction of the ch.f. of a PND. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I.  相似文献   

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