This article is cited in 3 papers

An extremal property of outer functions

B. I. Korenblum

Kiev State Technical University of Construction and Architecture

Abstract: Our main result is the following: if $f(z)$ is in the space $H^2$, and $F(z)$ is its outer part, then $\|F^{(n)}\|_{H^2}\le\|f^{(n)}\|_{H^2}$ $(n=1,2,\dots)$, the left side being finite if the right side is finite. Under certain essential restrictions, this inequality was proved by B.I. Korenblyum and V.S. Korolevich [1].

UDC: 517.5

Received: 19.06.1970

 English version: Mathematical Notes, 1971, 10:1, 456–458

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