Integral means of derivatives of univalent functions in Hardy spaces
| Autor: | Pérez-González, Fernando, Rättyä, Jouni, Vesikko, Toni |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that the norm in the Hardy space $H^p$ satisfies \begin{equation}\label{absteq} \|f\|_{H^p}^p\asymp\int_0^1M_q^p(r,f')(1-r)^{p\left(1-\frac1q\right)}\,dr+|f(0)|^p\tag{\dag} \end{equation} for all univalent functions provided that either $q\ge2$ or $\frac{2p}{2+p} |
| Databáze: | arXiv |
| Externí odkaz: |
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