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We study linear extremal problems in the Bergman space $A^p$ of the unitdisc, where $1 < p < \infty$. 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 $q\le q_1 < \infty$ and $k \in H^{q_1}$, then $F \in H^{(p-1)q_1}$. This resultwas previously known only in the case where $p$ is an even integer. We alsodiscuss related results.

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's $H^p$ Regularity Theorem For $1