Extreme Points in H1(R)
1967 ◽
Vol 19
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pp. 312-320
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Keyword(s):
Let R be an open Riemann surface. ƒ belongs to H1(R) if ƒ is holomorphic on R and if the subharmonic function |ƒ| has a harmonie majorant on R. Let p be in R and define ||ƒ|| to be the value at p of the least harmonic majorant of |ƒ|. ||ƒ|| is a norm on the linear space H1(R), and with this norm H1(R) is a Banach space (7). The unit ball of H1(R) is the closed convex set of all ƒ in H1(R) with ||ƒ|| ⩽ 1. Problem: What are the extreme points of the unit ball of H1(R)? de Leeuw and Rudin have given a complete solution to this problem where R is the open unit disk (1).
1979 ◽
Vol 31
(1)
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pp. 9-16
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Keyword(s):
1994 ◽
Vol 49
(2)
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pp. 249-256
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Keyword(s):
1987 ◽
Vol 35
(2)
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pp. 267-274
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2012 ◽
Vol 2012
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pp. 1-20
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