Weighted norm inequalities for fractional oscillatory integrals and applications

TL;DR

This paper establishes weighted norm inequalities for fractional oscillatory integral operators and explores their applications to commutators with BMO functions, advancing understanding of these operators in harmonic analysis.

Contribution

The paper introduces new weighted norm inequalities for fractional oscillatory integrals and their commutators with BMO functions, expanding theoretical frameworks in harmonic analysis.

Findings

Weighted norm inequalities for fractional oscillatory integrals are proved.

Results are extended to commutators with BMO functions.

Applications demonstrate the utility of these inequalities in analysis.

Abstract

We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by $BMO(\mathbb{R}^{n})$ functions and the operators are established.