Vol. 105, No. 1, 1983

Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On the transformation of Fourier coefficients of certain classes of functions. II

Kenneth F. Andersen

Vol. 105 (1983), No. 1, 1–10
Abstract

If {aν}1 is the sequence of Fourier cosine coefficients of a function in the space Lp, 1 p < , a Theorem of Hardy states that the sequence of averages {j=1νaj)∕ν}1 arise as Fourier cosine coefficients of a function also in Lp. Analogous results for the sequence {Σj=νaj∕j}1 were obtained by Bellman. In this paper, sufficient conditions on the non-negative weight function ω(x) are given in order that the weighted Lebesgue space Lp(ω(x)dx) may replace the spaces Lp in the Theorems of Hardy and Bellman.

Mathematical Subject Classification 2000
Primary: 42A16
Secondary: 46E30
Milestones
Received: 19 August 1981
Published: 1 March 1983
Authors
Kenneth F. Andersen