Bounds of weighted Hardy-Cesaro operators on weighted Lebesgue and BMO spaces

This paper aims to investigate the norms of the weighted Hardy-Cesaro operator U(psi,s)f (x) = f(0)(1) f (s(t) . x) psi (t) dt on weighted Lebesgue and BMO spaces. Under certain conditions on s(t) and on omega, we characterize the weight function psi so that U-psi,U-s is bounded on L-p(omega), BMO(omega). The corresponding operator norms are worked out too. We also give a necessary condition on the weight function psi, for the boundedness of the commutators of operator U-psi,U-s on Lp(omega) with symbols in BMO(omega).