New convolutions for an oscillatory integral operator on the half-line

Abstract

The main purpose of this work is to present three new convolutions for oscillatory integral operators defined on the positive half-line and in the framework of L1 Lebesgue spaces. Therefore, such new functions introduced by the new convolutions will have factorization properties when considering the oscillatory integral operators under consideration. Moreover, some fundamental and operational properties of the mentioned integral operator are also studied in the first part of the paper.