In this chapter, we build some Hilbert-type integral inequalities with two pairs of conjugate
exponents and an independent parameter, and consider their operator characterizations. The equivalent
forms and the reverses are also given. Some sufficient conditions of bounded operator are established
and a number of particular inequalities are deduced. The proofs of some basic theorems are used the
limit theorems in the theory of Lebesgue integrals and the technique of real analysis.