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ABSTRACT Let be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group, its homogeneous norm and Q its homogeneous dimension. In this… Click to show full abstract
ABSTRACT Let be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group, its homogeneous norm and Q its homogeneous dimension. In this paper we prove the two weighted inequality for fractional integrals on . 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 is proved as an application of this result.
Journal Title: Integral Transforms and Special Functions
Year Published: 2017
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