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A half-discrete reverse Hilbert-type inequality with homogeneous kernel. (Chinese. English summary) Zbl 1349.26070

Summary: Using the way of weight functions and the idea of introducing parameters, we obtain a half-discrete reverse Hilbert-type inequality and its equivalent forms with a monotone decreasing homogeneous kernel and a best constant factor by introducing an independent parameter and two pairs of conjugate exponents. Moreover, we also consider two cases of \(0 < p < 1\) and \(p < 0\).

MSC:

26D15 Inequalities for sums, series and integrals