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We build a multiple Hilbert-type integral inequality with the symmetric kernel K(x,y) and involving an integral operator T. For this objective, we introduce a norm Ã¢ÂˆÂ¥xÃ¢ÂˆÂ¥ÃŽÂ±nÃ¢Â€Â‰Ã¢Â€Â‰(xÃ¢ÂˆÂˆÃ¢Â„Â+n), two pairs of conjugate exponents (p,q) and (r,s), and two parameters. As applications, the equivalent form, the reverse forms, and some particular inequalities are given. We also prove that the constant factors in the new inequalities are all the best possible

On a Multiple Hilbert-Type Integral Inequality with the Symmetric Kernel