ON MEANS OF BANACH-SPACE-VALUED FUNCTIONS

We continue to study relations among exponential and polynomial growth orders of the γ-th order Cesàro means (γ≥0) and of the Abel mean for a Banach-space-valued function u on the interval [0,∞). We have already studied the problem for a continuous function u. Now we assume that u is a locally integrable function in a Banach space or an improperly locally integrable positive function in a Banach lattice.