Product and Commutators of Pseudo-differential Operators Involving Fourier–Jacobi Transform

Abstract

The purpose of this paper is to define a new symbol class $\Lambda $ and discuss the theory of two different pseudo-differential operators (p.d.o.) involving Fourier–Jacobi transform associated with a single symbol in $\Lambda $. We also derive boundedness results for p.d.o.’s in Sobolev type space. A new pseudo-differential operator is developed using the product of symbols. Finally, norm inequality for commutators between two pseudo-differential operators is obtained.

Keywords

Jacobi functions / Fourier–Jacobi transform / Sobolev space / Pseudo-differential operators

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