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A reverse Hilbert-type inequality with several parameters. (Chinese. English summary) Zbl 1249.26032

Summary: A reverse Hilbert’s inequality of bi-parameter type is investigated by introducing two independent parameters \(\lambda_1\) and \(\lambda_2\) and one pairs of conjugate exponents \((p, q)\), and by using a weight function and the method of real analysis. A reverse Hilbert-type integral inequality with several parameters and a mixed kernel is obtained, and its constant factor is proved to be the optimal value. As applications, an equivalent form and the corresponding to the double series inequalities are established.

MSC:

26D15 Inequalities for sums, series and integrals
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