Open Access
Summer 2011 Extremal problems in Bergman spaces and an extension of Ryabykh’s theorem
Timothy Ferguson
Illinois J. Math. 55(2): 555-573 (Summer 2011). DOI: 10.1215/ijm/1359762402

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

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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

Information

Published: Summer 2011
First available in Project Euclid: 1 February 2013

zbMATH: 1276.30062
MathSciNet: MR3020696
Digital Object Identifier: 10.1215/ijm/1359762402

Subjects:
Primary: 30D60 , 30D65

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign

Vol.55 • No. 2 • Summer 2011
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