Image areas and $H_{2}$ norms of analytic functions
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- by Shōji Kobayashi PDF
- Proc. Amer. Math. Soc. 91 (1984), 257-261 Request permission
Abstract:
For an analytic function $f$ in the unit disc $U$ with $f(0) = 0$, the inequality $\left \| f \right \|_2^2 \leqslant \frac {1}{\pi }$ area $\{ f(U)\}$ is shown, where an equality occurs if and only if $f$ is a constant multiple of an inner function. As a corollary, it is shown that for an analytic function in a general domain the square of its ${H_2}$ norm is bounded by its Dirichlet integral, with the equality condition being settledReferences
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 257-261
- MSC: Primary 30D55; Secondary 30C80
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740181-4
- MathSciNet review: 740181