Holomorphic Functions with Positive Real Part
Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 1-7
Voir la notice de l'article provenant de la source Cambridge University Press
The main purpose of this note is to prove a special case of the following conjecture. Conjecture. If F is holomorphic on the unit ball Bn in C n and has positive real part, then F is in Hp(Bn) for 0 < p < 1⁄2(n + 1).Here Hp(Bn) (0 < p < ∞) denote the usual Hardy spaces of holomorphic functions on Bn. See below for definitions. We remark that the conjecture is known for 0 < p < 1 and that some evidence for it already exists in the literature; for example [1, Theorems 3.11 and 3.15] where it is shown that a particular extreme element of the convex cone of functions is in Hp (B 2) for 0 < p < 3/2.
Sawyer, Eric. Holomorphic Functions with Positive Real Part. Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 1-7. doi: 10.4153/CJM-1982-001-1
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author = {Sawyer, Eric},
title = {Holomorphic {Functions} with {Positive} {Real} {Part}},
journal = {Canadian journal of mathematics},
pages = {1--7},
year = {1982},
volume = {34},
number = {1},
doi = {10.4153/CJM-1982-001-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-001-1/}
}
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