Adams-Spanne type estimates for the commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups

TL;DR

This paper establishes BMO space estimates for commutators of fractional sublinear operators within generalized Morrey spaces on Heisenberg groups, using Zygmund-type inequalities to characterize boundedness.

Contribution

It introduces new boundedness conditions for these operators in the setting of Heisenberg groups, expanding the understanding of their behavior in generalized Morrey spaces.

Findings

BMO space estimates for commutators are derived.

Boundedness conditions are characterized by Zygmund-type inequalities.

Results extend the theory of fractional operators to non-commutative groups.

Abstract

In this paper we give BMO (bounded mean oscillation) space estimates for commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are also formulated in terms of Zygmund type integral inequalities.