In this chapter, by using the way of weight coefficients and the technique of real analysis, some basic theorems
and corollaries on the discrete Hilbert-type inequalities with the homogeneous kernel of degree -1 are given. We apply
some relating results mentioned in Chap ter 2 to building some Hilbert-type in equalities with a particular homogeneous
kernel of degree -1. The strengthened vers ions, the reverses and the more accurate Hilbert-type inequalities are considered.
The proofs about the best possible property of the constant factors are left in Chapter 4. In some particular examples of this
chapter, the improved Euler-Maclaurin summation formulas mentioned in Charter 2 and are used here.
