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Exposed points and extremal problems in H1

✍ Scribed by Takahiko Nakazi

Book ID
107794896
Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
319 KB
Volume
53
Category
Article
ISSN
0022-1236

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## Abstract An essential bounded function __Ο•__ gives a continuous linear functional on the Hardy space __H__^1^ on the bitorus. In this paper, we consider extremal problems on __H__^1^ when __Ο•__ is a rational function, __Ο•__ is a product of one variable functions or __Ο•__ = |__f__|/__f__ for some

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Let X be a complex Banach space and L 1 (X ) :=L 1 (T; X) the Bochner space on the circle T. The X-valued Hardy space , extremal kernels and functions for this duality are studied. Proximinality fails for X :=L 1 Γ‚H 1 0 ; this is equivalent to the assertion that for 4 := N\_Z \_ Z\_N, L 1 4 (T 2 )