U. Goginava

Cesaro Means of Trigonometric Fourier Series

abstract:
L. Zhizhiashvili proved that if f belongs to H_p^w for some p, 1 <= p <= infinity, and 0 < a < 1, then the L^p-deviation of f from its Cesaro mean is O(n^aw(1/n)) where w(.) is a modulus of continuity. We show that this estimation is non-amplifiable for p = 1.