Two versions of fractional powers of Hankel-type transformations and pseudo-differential operators

摘要

Two versions of the fractional powers of Hankel-type transformations are discussed on certain Zemanian type spaces. The operational formulae are developed. Pseudodifferential operators (p.d.o.) associated with the symbol a(x, y) are defined. Integral representation of p.d.o. are obtained. Using the fractional Hankel convolution it is shown that the p.d.o. satisfy the L _(ν,μ)~1 norm inequality. Finally these Hankel-type transformations are used in the solution of some partial differential equations.