Some sufficient conditions for uniform convergence of Fourier series (Q1100376)

In 1976 A. M. Garsia proved that if a function belongs to the Besov space then its Fourier series converges uniformly. In this paper the authors generalize the above result of Garsia by proving that if a function f on the unit circle belongs to the Besov space \(\wedge (1/p,p,1)\), where p is an index in the interval (2,\(\infty)\), then f belongs to the Figà- Talamanca space \(A_ p\). Their proof depends on well known notions of harmonic analysis while Garsia used a rearrangement inequality proved by combinatorial methods. The authors also study the connection between the results on uniform convergence and some conditions for integrability of sums of trigonometric series.