Let D denote the unit disc in C. We define the generalized Cesàro operator as follows:
Cω( f )(z) =
1
0
f (t z)
1
z
z
0
Bω
t (u) du
ω(t)dt,
where {Bω
ζ }ζ∈D are the reproducing kernels of the Bergman space A2
ω induced by a
radial weight ω in the unit disc D. We study the action of the operator Cω on weighted
Hardy spaces of analytic functions Hγ , γ > 0 and on general weighted Bergman
spaces A2
μ
