Composition of pseudodifferential operators associated with fractional Hankel–Clifford integral transformations

Abstract

Two versions of pseudodifferential operators (pdo) involving fractional powers Hankel–Clifford integral transformations are defined. The composition of first and second fractional pdo is defined. We show that the pdo and composition of pdo are bounded in a certain Sobolev-type space associated with the fractional powers of Hankel–Clifford integral transformations. Some special cases are also discussed.

Keywords:

• pseudodifferential operator
• Zemanian space
• fractional Hankel–Clifford transformation
• fractional Hankel–Clifford convolution
• Sobolev-type space

AMS Subject Classifications:

• Primary: 46F05
• 46F12
• 47G30; Secondary: 35S05
• 46E10
• 46E35

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NBHM(DAE) projects Govt. of India, [grant number 2/48(14)/2011/-R&D II/3501].