EMBEDDINGS BETWEEN WEIGHTED TANDORI AND CESARO FUNCTION SPACES

We characterize the weights for which the two-operator inequality ||(integral(x)(0) f(t)(p) upsilon(t)(p) dt) (1/p)||(q,u,(0,infinity)) <= c||(t is an element of(x,infinity))ess sup f(t)||(r,w,(0,infinity)) holds for all non-negative measurable functions on (0;1), where 0 < p < q <= infinity and 0 < r < infinity, namely, we.nd the least constants in the embeddings between weighted Tandori and Cesaro function spaces. We use the combination of duality arguments for weighted Lebesgue spaces and weighted Tandori spaces with weighted estimates for the iterated integral operators