L1-convergence of fourier series with complex quasimonotone coefficients
Abstract
A sequence of Fourier coefficients {ƒ(w)} of a complex function in L1(T) is said to be complex quasimonotone if there exists 60 such thatA ƒ (”)+ ƒG {zl} for some a ^ 0 and for all n. It is proved that Fourier series with asymptotically even and complex quasimonotone coefficients, satisfying IS n’^ max \*f(j)\’/q mjuc \f(j)\’/P = o(l). A-*l+0, j; + J=l, converges in L (7’)-norm if and only if /(w)lg | n\= o(l), n -> oo. A recent result of t. V. Stanojevic [3] is a special case of the corollary of the main theorem.
Document Type
Article
DOI
https://doi.org/10.1090/S0002-9939-1982-0667282-1
Publication Date
1-1-1982
Recommended Citation
Stanojevic, Vera B. "��¹-convergence of Fourier series with complex quasimonotone coefficients." Proceedings of the American Mathematical Society 86, no. 2 (1982): 241-247.
Journal Title
Proceedings of the American Mathematical Society
