The Hilbert-type integral inequalities with a homogeneous kernel of -λ-degree

By introducing an integral operator, a norm with a weight function, and two pairs of conjugate exponents, we find the conditions for the Hilbert-type integral inequalities with a homogeneous kernel of -lambda- degree. We also prove that the constant factors in the inequalities are all the best possible. As the particular situations, some new inequalities with a homogeneous kernel and their other two forms are given. We extend some previous results.