Univalent Functions, <Emphasis Type="Italic">VMOA</Emphasis> and Related Spaces |
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| Authors: | Petros Galanopoulos Daniel Girela Rodrigo Hernández |
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| Institution: | 1.Departamento de Análisis Matemático, Universidad de Málaga,Facultad de Ciencias, Campus de Teatinos,Málaga,Spain;2.Facultad de Ingeniería y Ciencias,Universidad Adolfo Ibá?ez,Vi?a del Mar,Chile |
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| Abstract: | This paper is concerned mainly with the logarithmic Bloch space ℬlog which consists of those functions f which are analytic in the unit disc
\mathbbD{\mathbb{D}} and satisfy
sup|z| < 1(1-|z|)log\frac11-|z||f￠(z)| < ￥\sup_{\vert z\vert <1}(1-\vert z\vert )\log\frac{1}{1-\vert z\vert}\vert f^{\prime}(z)\vert <\infty , and the analytic Besov spaces B
p
, 1≤p<∞. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We
give explicit examples of:
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A bounded univalent function in $\bigcup_{p>1}B^{p}$\bigcup_{p>1}B^{p} but not in the logarithmic Bloch space. |
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| Keywords: | |
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