International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 8, Pages 407-419
doi:10.1155/S0161171204212388
The pseudodifferential operator A(x,D)
Department of Mathematics, Banaras Hindu University, Varanasi 221005, India
Received 16 December 2002
Copyright © 2004 R. S. Pathak and S. Pathak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The pseudodifferential operator (p.d.o.) A(x,D), associated with the Bessel operator d2/dx2+(1−4μ2)/4x2, is defined. Symbol class Hρ,δm is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space Hμ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution Lσ,αp-norm continuity of the p.d.o. is proved.