Commutators of multilinear θ-type generalized fractional integrals on non-homogeneous metric measure spaces

Abstract

Let $ {\mathcal{I}_{\alpha, m}} $ be the multilinear $ \theta $-type generalized fractional integrals and $ \vec{b}_{\sigma} $ be the vector with each $ b_{\sigma_{i}} \in \widetilde{{\rm{RBMO}}}\left(\mu\right) $. The boundedness for $ {\mathcal{I}_{\alpha, m}} $ and the iterated multi-commutators $ {\mathcal{I}_{\alpha, m, \vec{b}_\sigma}} $ on Lebesgue spaces over non-homogeneous spaces are showed in this paper.

Keywords

• multilinear θ-type generalized fractional integrals
• iterated commutators
• non-homogeneous measures
• boundedness
• lebesgue spaces