Integral properties of generalized Bessel potentials

The study on the space of generalized Besel potentials in Euclidean n-space Rn is discussed. The Euclidian n-space is defined as a function of Besel-Macdonald kernel and Macdonald function. The rearrangement invariant space (RIS) class includes the Lp, Lorentz, Marcinkiewicz, and Orlicz spaces. Embedding theory for classical Besel potentials and their weighted generalizations is exposed in Maz'ya's survey. The problems are posed by Netrusov. An important role is played by estimates for convolution decreasing rearrangements obtained by O'Neil. The results are concretized and the rearrangement invariant hull of the potential space is described.