We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basi...We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.1147103911271162 and 11561062)
文摘We investigate a class of multilinear integral operators with the nonnegative kernels, and prove that the norms of the operators can be obtained by integral of the product of the kernel function and finitely many basic functions. Using the integral, we can easily calculate the sharp constants for the multilinear Hilbert inequality, the generalized Hardy-Littlewood-Sobolev inequality and the multilinear Hardy operator.
