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Research Article

Canonical potential and Lp-Sobolev space involving linear canonical Fourier transform

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Pages 295-315 | Received 01 Mar 2021, Accepted 25 Aug 2022, Published online: 12 Sep 2022
 

Abstract

The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential Jm,A and corresponding Lp-Sobolev space. Moreover, the Schwartz-type space SA is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The Lp-boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces HAm,p and HAm,p are given.

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Acknowledgments

Authors are very thankful to the reviewers for his/her valuable and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by Department of Science andTechnology, Ministry of Science and Technology, india , under grant  no. DST/INSPIRE Fellowship/2017/IF170292.

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