**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^{a}w(1/n))
where w(.) is a modulus of continuity. We show that
this estimation is non-amplifiable for p = 1.