Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This 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

T. Sheil-Small
Proceedings of the American Mathematical Society
Vol. 88, No. 2 (Jun., 1983), pp. 275-282
DOI: 10.2307/2044716
Stable URL: http://www.jstor.org/stable/2044716
Page Count: 8
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
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
Preview not available

Abstract

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).

Page Thumbnails

  • Thumbnail: Page 
275
    275
  • Thumbnail: Page 
276
    276
  • Thumbnail: Page 
277
    277
  • Thumbnail: Page 
278
    278
  • Thumbnail: Page 
279
    279
  • Thumbnail: Page 
280
    280
  • Thumbnail: Page 
281
    281
  • Thumbnail: Page 
282
    282