Factors for \(|\overline N,p_ n;\delta|_ k\) summability of Fourier series
The author first establishes a theorem on summability factors of a series \(\sum a_ n\) for \(| \overline N,p_ n;\delta |_ k\) summability. He then uses it to obtain a result for Fourier series of \(f(x)\) under the condition ``\(\varphi_ 1(t) \in BV(0,\pi)\)'', where \(\varphi_ 1(t)={1 \over 2t} \int^ t_ 0\{f(x+u)+f(x-u)\}du\). These results extend his previous results [Bull. Inst. Math., Acad. Sin. 17, No. 3, 285-290 (1985; Zbl 0696.42007)] on summability \(| \overline N,p_ n |_ k\), \(k \geq 1\).
scientific article; zbMATH DE number 92805