Negative eigenvalues of the Schroedinger equation: An approach through fractional integration and Morrey spaces

The time independent Schrodinger equation has been analyzed for singular potentials. Direct estimates of the solution of the Schrodinger equation and estimates of the negative eigenvalues of the Schrodinger operator are obtained for potentials in certain Morrey spaces and for potentials of divergence form.; The method of solution relies heavily on an extension of the Hardy-Littlewood-Sobolev inequality. This fractional integral inequality enables one to reproduce classical results for the negative eigenvalues by Fefferman-Phong, and to find direct estimates for potentials of divergence form.