Kôsi Kanno

On the absolute Nörlund summability factors of a Fourier series and its conjugate series at a point

The object of this paper is to give generalizations of Okuyamas Theorem [ Bull. Austral. Math. Soc. 12 (1975), 9–21, Toohoku Math. J. (2) 28 (1976), 563–581] on the absolute Norlund summability factors of a Fourier series and its conjugate series. Our theorems imply many results proved by other authors: especially Theorem 1 includes the results of Bhatt and Kishor [ Indian J. Math. 9 (1967), 259–267 (1968)], Dikshit [ Pacific J. Math. 63 (1976), 371–379], and Lal [ Publ. Inst. Math. ( Beograd ) 20 ( 34 ) (1976), 169–178], and we can easily deduce Lals result [ Indian J. Math. 16 (1974), 1–22] from our Corollary 2.