 |
|
On the Smirnov Class Defined by the Maximal Function |
Canad. Math. Bull. 45(2002), 265-271
Published:2002-06-01
Printed: Jun 2002
Printed: Jun 2002
- Marek Nawrocki
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 30A78 30A76 - unknown classification 30A76 |