Fractional Oscillatory Integral Operators and Their Commutators on Generalized Orlicz-Morrey Spaces of the Third Kind

Abstract

We deal with the generalized Orlicz-Morrey space \(M_{\Phi,\varphi}\) of the third kind and consider the boundedness of the oscillatory integral operators and fractional oscillatory integral operators on \(M_{\Phi,\varphi}\). Some integral estimates for generalized Orlicz-Morrey spaces of the third kind are also obtained by using weighted Hardy operators. The corresponding commutators generated by \(BMO\)-functions are also considered.