Geodesic
Extreme Points in H1(R)
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 312-320

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Forelli, Frank. Extreme Points in H1(R). Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 312-320. doi: 10.4153/CJM-1967-022-0
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[1] 1. de Leeuw, K. and Rudin, W., Extreme points and extremum problems in H , Pacific J. Math., 8 (1958), 467–485. Google Scholar

[2] 2. Forelli, F., Invariant subspaces in L1 , Proc. Amer. Math. Soc., 14 (1963), 76–79. Google Scholar

[3] 3. Forelli, F., Bounded holomorphic functions and projections, Illinois J. Math., 10 (1966), 367–380. Google Scholar

[4] 4. Gamelin, T., Extreme points in spaces of analytic junctions (unpublished). Google Scholar

[5] 5. Hoffman, K., Banach spaces of analytic functions (Englewood Cliffs, N.J., 1962). Google Scholar

[6] 6. Loève, M., Probability theory (Princeton, 1955). D. Van Nostrand Company. Google Scholar

[7] 7. Rudin, W., Analytic functions of class H , Trans. Amer. Math. Soc., 78 (1955), 46–66. Google Scholar

[8] 8. Zygmund, A., Trigonometric series, vol. 1 (Cambridge, 1959). Google Scholar

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