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Extremal problems for summable analytic functions. (Russian) Zbl 0622.30032

Let \(A_ p\) be the space of functions analytic in the unit disc \({\mathbb{D}}\) and summable in the power p. Given a polynomial \(\omega (z)=\sum^{n}_{k=0}\omega_ kz^ k\), the author investigates the extremal function of the functional on \(A_ p:\) \[ f\mapsto \iint_{{\mathbb{D}}}f(z){\bar \omega}(z) dx dy. \]
Reviewer: V.V.Peller

MSC:

30D55 \(H^p\)-classes (MSC2000)

Keywords:

Bergman class
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