1 results
On the Smirnov Class Defined by the Maximal Function
-
- Journal:
- Canadian Mathematical Bulletin / Volume 45 / Issue 2 / 01 June 2002
- Published online by Cambridge University Press:
- 20 November 2018, pp. 265-271
- Print publication:
- 01 June 2002
-
- Article
-
- You have access
- Export citation
-
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 $.
