Composition of Pseudo-Differential Operators Associated with Jacobi Differential Operator

摘要

abstract_textpUsing inverse Fourier-Jacobi transform two symbols are defined and two pseudo-differential operators (p.d.o.'s) P-alpha,P-beta(x, D) and Q(alpha,beta)(x, D) are introduced. Composition of P-alpha,P-beta(x, D) and Q(alpha,beta)(x, D) is defined. It is shown that the p.d.o.'s and composition of p.d.o.'s are bounded in a Sobolev type space. Some special cases are discussed./p/abstract_text