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By using the way of weight coefficient and the theory of operators, we define a Hilbert-type operator with a class of homogeneous kernels and obtain its norm. As applications, an extended basic theorem on Hilbert-type inequalities with the decreasing homogeneous kernels of −λ-degree is established, and some particular cases are considered.doi:10.1155/2009/572176 fatcat:zfm2h7ff4bbzpbj6f6gvrl2hxm