Sobolev type spaces associated with Bessel operators

[摘要] A Sobolev type space G(mu)(s,p) is defined and its properties including completeness and inclusion are investigated using the theory of distributional Hankel transform. The Hankel potential H-mu(s) is defined. It is shown that the Hankel potential H-mu(s) is a continuous linear mapping of the Zemanian space H-mu into itself. The LP-space of all such Hankel potentials, W-mu(s,p) (0,infinity) is defined. It is shown that W-mu(s,p) is a Banach space with respect to the norm parallel to parallel to(s,p,mu). It is also shown that the Hankel potential is an isometry of W-mu(s,p). An L-p-boundedness result for the Hankel potential is proved. It is shown that solutions of certain nonhomogeneous equations involving Bessel differential operators belong to these spaces. (C) 1997 Academic Press.

[发布日期] 1997-11-01