On the cones of rearrangements for generalized bessel and Riesz potentials

In this article, we study the spaces of potentials in n-dimensional Euclidean space. They are constructed on the basis of a rearrangement invariant space by using convolutions with some general kernels. Specifically, the treatment covers spaces of classical Bessel and Riesz potentials. We establish the equivalent characterization for the cones of decreasing rearrangements of potentials. This is the key result for description of integral properties of potentials. © 2010 Taylor & Francis.