Abstract
We study linear extremal problems in the Bergman space $A^p$ of the unit disc for $p$ an even integer. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if the Taylor coefficients of $k$ are sufficiently small, then the extremal function $F \in H^{\infty}$. We also show that if $q \le q_1 < \infty$, then $F \in H^{(p-1)q_1}$ if and only if $k \in H^{q_1}$.
Citation
Timothy Ferguson. "Extremal problems in Bergman spaces and an extension of Ryabykh’s theorem." Illinois J. Math. 55 (2) 555 - 573, Summer 2011. https://doi.org/10.1215/ijm/1359762402
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