Commutators of the fractional maximal function in generalized Morrey spaces on Carnot groups

Abstract

In this paper, we obtain new results of the Spanne and Adams type boundedness characterization of the fractional maximal commutator operator $M_{b,\alpha }$, $0\le \alpha <Q$ on the Carnot group $\mathbb{G}$ (i.e. nilpotent stratified Lie group) in generalized Morrey spaces $M_{p,\varphi }\left(\mathbb{G}\right),$ respectively, where Q is the homogeneous dimension of $\mathbb{G}$.

Keywords:

• Carnot group
• fractional maximal function
• generalized Morrey space
• commutator
• BMO

AMS Subject Classifications:

• Primary 42B25
• 42B35
• 43A15
• 43A80

Acknowledgments

The author like to express thanks to the referees for their kind comments and helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by the grant of Cooperation Program 2532 TUBITAK – RFBR (RUSSIAN foundation for basic research) (Agreement number no. 119N455) and by Department of Mathematics Analysis and the Theory of Functions, Peoples' Friendship University of Russia, Moscow, Russia.