Asymptotic behavior of trigonometric series with O-regularly varying quasimonotone coefficients

[摘要] In this paper, the asymptotic behavior of a trigonometric series with O-regularly varying quasimonotone coefficients is investigated. Our results generalize the work done by S. Aljancic, R. Bojanic, and M. Tomic (1956, Publ. hst. Math. (Beograd) (N.S.) 10, 101-120), R. Bojanic and J. Karamata (1963, Tech Rep 432, Math Research Center, Madison, WI), G. H. Hardy (1928, J. London Math Sec. 3, 12-13; 1931, Proc. London Math. Sec. (2) 32, 441-448), G. H. Hardy and W. W. Rogosinski (1945, Quart. J. Math. Oxford 16, 49-58), J. R. Nurcombe (1993, J. Math. Anal. Appl. 178, 63-69), C. H. Yong (1969, Publ. Inst. Math. (Beograd) (N.S.) 9, 29-35), and A. Zygmund (1968, Trigonometric Series, Vol. 1, 2nd ed., Cambridge Univ. Press, Cambridge, UK). (C) 2000 Academic Press.

[发布日期] 2000-10-01