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On a Hilbert-type linear series operator and its applications. (English) Zbl 1205.47011
A Hilbert-type linear series operator and its norm are studied. In particular, several generalizations of Hilbert-type inequalities whose kernels are symmetric and homogeneous of the first order are presented and discussed. Furthermore, the reverse forms of Hilbert-type inequalities are also derived and several consequences of the obtained results are pointed out.
MSC:
47A30Operator norms and inequalities
26D15Inequalities for sums, series and integrals of real functions
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