Some Classes of L 1-Convergence of Fourier Series
Tóm tắt
In this paper equivalent classes of the classes M′α and S′
pαr
, p > 1, α > 0. r ∈ { 0,1,2, ... ,[α]} defined by Shuyun [3] are obtained. Then, it is shown that the class S
pαr
, 1 > p ≤ 2, α ≥ 0, r ∈ {0,1,2,...,[α]} is a subclass of BV∩C
r
, where S
pαr
is the equivalent class of the Shuyun's class S′
pαr
, BV is the class of null sequences of bounded variation and C
r
is the extension of the Garrett--Stanojevic class. As a corollary of this result, we have obtained the theorem, proved in [7].
Tài liệu tham khảo
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Ž. Tomovski, An extension of the Garrett-Stanojevic class, Approx. Theory & Appl. 16(1), 46-51 (2000), [ONLINE] A corrected version is available in the RGMIA Research Report Collection, 3(4), Article 3, 2000, URL: http://zgmia.vu.edu.au/v3n4.html. Some Classes of L1-Convergence of Fourier Series 89