Expansions, inequalities and approximations.
On the occasion of Gavin Brown’s 65th Birthday
University of Sydney, Australia, 5-6 March 2007
f with absolutely convergent Fourier series.
We give best possible sufficient conditions in terms of the Fourier coefficients of f in order that f belong either
to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes Zyg(α)
and zyg(α) for some 0 < α ≤ 2. The termwise differentiation of Fourier series is also discussed.
Our theorems generalize some of those proved by R.P. Boas Jr., J. Németh and R.E.A.C. Paley.