Abstract
In 1958 Carleson proved that a sequence is interpolating if it is uniformly separated,
later in 1983 Peter Jones gave a simple constructive proof in [JON] which
is stunning in his time. On the other hand, when a sequence is not uniformly
separated, Garnett gave a sharp positive result in [GAR2]. Following Jones's
idea in [JON] and also a highly relevant paper [VIN] due to Vinogradov, we
give a constructive proof to Garnett's result on nonuniformly separated sequence
with slightly modified assumption. We will also discuss extremal problems that
is described in the language of Hardy spaces and solve it in functional analytical
point of view.
Post a Comment