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# On the Smirnov Class Defined by the Maximal Function

Published:2002-06-01
Printed: Jun 2002
• Marek Nawrocki
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## Abstract

H.~O.~Kim has shown that contrary to the case of $H^p$-space, the Smirnov class $M$ defined by the radial maximal function is essentially smaller than the classical Smirnov class of the disk. In the paper we show that these two classes have the same corresponding locally convex structure, {\it i.e.} they have the same dual spaces and the same Fr\'echet envelopes. We describe a general form of a continuous linear functional on $M$ and multiplier from $M$ into $H^p$, $0 < p \leq \infty$.
 Keywords: Smirnov class, maximal radial function, multipliers, dual space, Fréchet envelope
 MSC Classifications: 46E10 - Topological linear spaces of continuous, differentiable or analytic functions 30A78 - unknown classification 30A7830A76 - unknown classification 30A76

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