V.S.Guliyev, A. Eroglu, Y.Y.Mammadov, Riesz potential on the Heisenberg group and generalized Morrey spaces. Journal of Mathematical Sciences, Vol. 189, No. 3, March, 2013, 365-382 (original) (raw)

We consider the Riesz potential operator I α , on the Heisenberg group H n in generalized Morrey spaces M p,ϕ (H n) and find conditions for the boundedness of I α as an operator from M p,ϕ 1 (H n) to M p,ϕ 2 (H n), 1 < p < ∞, and from M 1,ϕ 1 (H n) to a weak Morrey space W M 1,ϕ 2 (H n). 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 H n , we prove two Sobolev-Stein embedding theorems for generalized Morrey and Besov-Morrey spaces. Bibliography: 40 titles.