Riesz potential in generalized Morrey spaces on the Heisenberg group

Abstract

We consider the Riesz potential operator I?, on the Heisenberg group Hn in generalized Morrey spaces Mp,?(Hn) and find conditions for the boundedness of I? as an operator from Mp,?1(Hn) to Mp,?2(Hn), 1 < p < ?, and from Mp,?1(Hn) to a weak Morrey space WM1,?2(Hn). The boundedness conditions are formulated it terms of Zygmund type integral inequalities. Based on the properties of the fundamental solution of the sub-Laplacian on Hn, we prove two Sobolev-Stein embedding theorems for generalized Morrey and Besov-Morrey spaces. Bibliography: 40 titles. © 2013 Springer Science+Business Media New York.