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Extremal problems in Hp

Published online by Cambridge University Press:  09 April 2009

Takahiko Nakazi
Affiliation:
Faculty of ScienceHokkaido UniversitySapporo 060, Japan
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Abstract

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Let 1≤p <∞ and 1/p+1/q = 1. If φ ∈ Lq, we denote by Tφ the functional defined on the Hardy space Hp by . A function f in Hp, which satisfies Tpφ(f) = ‖Tpφ‖ and ‖f‖p ≤ 1, is called an extremal function. Also, φ is called an extremal kernel when ‖φ‖q =‖Tpφ‖. In this paper, using the results in the case of p = 1, we study extremal kernel and extremal functions for p > 1.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

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