Pseudo-Differential Operators Associated with Modified Fractional Derivatives Involving the Fractional Fourier Transform.

Abstract

In this paper, properties of the n-dimensional fractional Fourier transform are discussed, and exploiting this theory, the continuity property on Schwartz space S(Rn) and its dual S′(Rn) are obtained. The pseudo-differential operators involving n-dimensional fractional Fourier transform are introduced. The continuity properties of pseudo-differential operators on S(Rn) and S′(Rn) are found. Sobolev type space associated with pseudo-differential operators involving the fractional Fourier transform is investigated and the boundedness of pseudo-differential operators on Sobolev type space is obtained. Applications of pseudo-differential operators associated with modified fractional derivative operator Dβα and modified fractional integral operator Iβα on the Lizorkin space Φ (R) are given. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.