Necessary conditions for a norm estimate of Riesz potential on Morrey spaces over hypergroups

摘要

Necessary conditions for a norm estimate of Riesz potential will be presented on Morrey spaces over commutative hypergroups by taking into account the upper Ahlfors condition. This norm estimate is the Hedberg type estimate. By assuming that the weak estimate of maximal operator holds in Morrey spaces over commutative hypergroups, the Hedberg type estimate leads to the weak estimate of the Riesz potential.