Subordination by Univalent H1 Functions
Abu‐Muhanna, Yusuf; Hallenbeck, D. J.
1987-05-01 00:00:00
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.pngBulletin of the London Mathematical SocietyWileyhttp://www.deepdyve.com/lp/wiley/subordination-by-univalent-h1-functions-eEjIBAQn3q
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 Society
– Wiley
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