Relationships among the terms in the expansions of the kinetic- and exchange-correlation-energy density functionals

With use of the Sobolev-H\"older inequalities, certain rigorous interrelationships among the leading terms in the expansions of the kinetic- and the exchange-correlation-energy density functionals have been derived. This work has also been extended to include some quasiclassical connections. All these relationships are inequalities that have been tested numerically with use of Hartree-Fock densities for 1806 neutral atoms and their ions.