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On the Smirnov Class Defined by the Maximal Function

Published online by Cambridge University Press:  20 November 2018

Marek Nawrocki
Marek Nawrocki*
Affiliation:
Faculty of Mathematics and Informatics, A. Mickiewicz University, ul. Matejki 48/49, 60-769 Poznán, Poland, e-mail: nawrocki@amu.edu.pl
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Abstract

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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, i.e. they have the same dual spaces and the same Fréchet envelopes. We describe a general form of a continuous linear functional on $M$ and multiplier from $M$ into ${{H}^{p}},\,0\,<\,p\,\le \,\infty $.

Keywords

46E1030A7830A76Smirnov classmaximal radial functionmultipliersdual spaceFréchet envelope
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 265 - 271
Copyright
Copyright © Canadian Mathematical Society 2002

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