Boundedness of oscillatory integral operators and their commutators on weighted Morrey spaces

TL;DR

This paper proves the boundedness of oscillatory and fractional oscillatory integral operators, along with their commutators generated by BMO functions, on weighted Morrey spaces, advancing understanding of their behavior in these function spaces.

Contribution

It establishes the boundedness of these operators and their commutators on weighted Morrey spaces, a novel extension in the field.

Findings

Oscillatory integral operators are bounded on weighted Morrey spaces.

Fractional oscillatory integral operators are bounded on these spaces.

Commutators generated by BMO functions are also bounded on weighted Morrey spaces.

Abstract

It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.