J Austral Math Soc Ser A 52 pp103--110, 1992.

External Problems in H^p

Takahiko Nakazi

Abstract

Let 1 £ p < ¥ and 1/p + 1/q = 1. If f Î L^q, we denote by T_f the functional defined on the Hardy space H^p by

Tfp(f) = ó õ p -p  f(eiq)f(eiq)dq/2p.

A function f in H^p, which satisfies T_f^p(f) = ||T_f^p|| and ||f||_p £ 1, is called an extremal function. Also, f is called an extremal kernel when ||f||_q = ||T_f^p||. In this paper, using the results in the case of p = 1, we study extremal kernels and extremal functions for p > 1.

1991 AMS Subject Classification: 30D05, 46J15

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Authors

Takahiko Nakazi

Facualty of Science, Hokkaido University, Sapporo 060, Japan.