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Two weighted inequalities for fractional integrals on Laguerre hypergroup
(Taylor & Francis Ltd, 2017) Eroglu, A.; Hajibayov, M. G.
Let K = [0,infinity) x R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group, vertical bar.vertical bar its homogeneous norm and Q its homogeneous dimension. In this paper we prove the two weighted inequality for fractional integrals I-beta on K. The obtained result is an analog of the Heinig result [Heinig HP. Weighted norm inequalities for classes of operators. Indiana Univ Math J. 1984;33(4):573-582] for fractional integrals on Laguerre hypergroup. Furthermore, the Stein-Weiss inequality for I-beta is proved as an application of this result.