Vanishing generalized Morrey spaces and commutators of Marcinkiewicz integrals with rough kernel associated with Schr\"odinger operator

TL;DR

This paper investigates the boundedness of commutators of Marcinkiewicz integrals with rough kernels linked to Schrödinger operators within vanishing generalized Morrey spaces, expanding understanding of harmonic analysis in quantum contexts.

Contribution

It introduces new boundedness results for these commutators on vanishing generalized Morrey spaces, connecting Schrödinger operators with harmonic analysis tools.

Findings

Boundedness of commutators established

Results apply to Schrödinger operators with reverse Hölder potential

Enhances understanding of harmonic analysis in quantum mechanics

Abstract

Let L=-{\Delta}+V(x) be a Schrodinger operator, where {\Delta} is the Laplacian on while nonnegative potential V(x) belonging to the reverse Holder class. We establish the boundedness of the commutators of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator on vanishing generalized Morrey spaces.