Optimal embedding of Bessel- and Riesz-type potentials

A study was conducted to deal the spaces of Bessel- and Riesz type potentials in the n dimensional Euclidean space Rn. Constructive criteria for embeddings in rearrangement invariant spaces were obtained and optimal RISes were described for such embeddings for the potentials. The results were based on the general ones presented in the first equation, which reduce the embedding of potentials to the description of the action of combined Hardy type operators on the half line R+ = (9, ∞). These results were also based on new order sharp estimates for the norms of these operators on cones of monotonic functions.