A STUDY OF NORM INEQUALITIES AND SOBOLEV SPACES USING PSEUDO-DIFFERENTIAL OPERATORS WITH HANKEL-CLIFFORD TRANSFORM
By
Balasaheb B. Waphare1,*, Rahilanaz Z. Shaikh2 and Nitin Rane3
1,2MAEER’s MIT Arts, Commerce & Science College, Alandi(D), Pune, Maharashtra, India-412105
3Avantika University, Ujjain, Madhya Pradesh, India-456006.
Email: balasahebwaphare@gmail.com, shaikhrahilanaz@gmail.com, vc@avantika.edu.in
(Received: May 07, 2024; In format: May 11, 2024; Revised: November 09, 2024; Accepted: November 19, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54222
Abstract
In this paper, we demonstrate that pseudo-differential operators h1,α,β satisfy a certain L1 α,β-norm inequality when using the Hankel-Clifford convolution. Also the properties of Sobolev-type space Gs,2α,β are studied in relation to the Hankel-Clifford transformation.
2020 Mathematical Sciences Classification: 46F05, 46F12.
Keywords: Hankel-Clifford transformation, Pseudo-differential operator, Sobolev-type space, Norm inequality.