Vol. 91, No. 2, 1980

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
|C, 1| summability of series associated with Fourier series

H. P. Dikshit and S. N. Dubey

Vol. 91 (1980), No. 2, 277–279
Abstract

The purpose of this paper is to prove the following theorem. Suppose that for u n0, g(u) and d(u) are positive functions such that ud(u) is nondecreasing and (i) n1g(n)d(n) < . Then the series d(n)An(x) is summable |C,1|, if the following hold:

      ∫
t               −1
Φ(t) = 0 |φ(u)|du = O (tg(t )), t −→ +0;          (1.1)

∑                  ∑         ∫ π
n−1d(n )I(n−1) =    n−1d(n)    t−1|φ(t)|dt < ∞.      (1.2)
n−1

Mathematical Subject Classification
Primary: 42A28
Milestones
Received: 5 June 1979
Revised: 18 September 1979
Published: 1 December 1980
Authors
H. P. Dikshit
S. N. Dubey