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Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function. (English) Zbl 1371.26036

Summary: By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardy-type integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.

MSC:

26D15 Inequalities for sums, series and integrals
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