Title

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

Journal Title

Proceedings of the American Mathematical Society

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