Pointwise and integral estimates for the $B$-Riesz potential in terms of $B$-maximal and $B$-fractional maximal functions

We study the maximal and fractional maximal functions and Riesz potentials that are generated by the generalized shift operator associated with the Laplace–Bessel operator. We obtain some pointwise and integral estimates that give a relation between the $B$-maximal and $B$-fractional maximal functions and $B$-Riesz potentials and extend the available results to the objects of a more general nature. Basing on these results, we prove interpolation theorems for the $B$-fractional maximal functions and $B$-Riesz potentials.