Commutators of Littlewood-Paley gκ∗ $g_{\kappa}^{*} $-functions on non-homogeneous metric measure spaces

Abstract

Abstract:The main purpose of this paper is to prove that the boundedness of the commutator M Ä;b generated by the Littlewood-Paley operator M Ä and RBMO. / function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of M Ä satisfies a certain Hörmander-type condition, the authors prove that M Ä;b is bounded on Lebesgue spaces L p . / for 1 < p < 1, bounded from the space L log L. / to the weak Lebesgue spaceL 1;1 . /, and is bounded from the atomicHardy spaces H 1 . / to the weak Lebesgue spaces L 1;1 . /.