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Subordination by Univalent H1 Functions

Subordination by Univalent H1 Functions Suppose that F is an element of H1 (Hardy class of order 1 over the unit disc) and F is a univalent starlike mapping. Let s(F) denote the set of functions subordinate to F and Hs(F) the closed convex hull of s(F). We prove that f ∈Hs(F) and ‖f‖1 = ‖F‖1 then f is an element of s(F). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/19.3.249
Publisher site
See Article on Publisher Site

Abstract

Suppose that F is an element of H1 (Hardy class of order 1 over the unit disc) and F is a univalent starlike mapping. Let s(F) denote the set of functions subordinate to F and Hs(F) the closed convex hull of s(F). We prove that f ∈Hs(F) and ‖f‖1 = ‖F‖1 then f is an element of s(F).

Journal

Bulletin of the London Mathematical SocietyWiley

Published: May 1, 1987

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