You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Coefficients and Integral Means of Some Classes of Analytic Functions
Proceedings of the American Mathematical Society
Vol. 88, No. 2 (Jun., 1983), pp. 275-282
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044716
Page Count: 8
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
The sharp coefficient bounds for the classes Vk of functions of bounded boundary rotation are obtained by a short and elementary argument. Elementary methods are also applied for the coefficients of related classes characterised by a generalised Kaplan condition. The result (1 + xz)α(1 - z)-β ≪ (1 + z)α(1 - z)-β (|x| = 1, α ⩾ 1, β ⩾ 1) is proved simply. It is further shown that the functions (1 + z)α(1 - z)-β are extremal for the pth means (p an arbitrary real) of all Kaplan classes K(α, β).
Proceedings of the American Mathematical Society © 1983 American Mathematical Society