A class of pseudo-differential operators associated with Bessel operators

[摘要] A class of pseudo-differential operators (p.d.o.), generalizing Bessel differential operator d(2)/dx(2) + (1 - 4 mu(2))/(4x(2)), is defined. Symbol classes H-m and H-o(m) are introduced. It is shown that p.d.o.'s associated with symbols belonging to these classes are continuous linear mappings of the Zemanian space H-mu into itself. An integral representation of p.d.o.'s is obtained. Using Haimo's theory of the Hankel convolution it is shown that p.d.o.'s satisfy a certain L(1) - norm inequality. (C) 1995 Academic Press, Inc.

[发布日期] 1995-12-01