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Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls. (English) Zbl 0948.26015

The authors introduce two types of multidimensional integral means of arbitrary real order with power weights, and prove corresponding mixed-means inequalities. The idea of introducing mixed-means with applications to derive Hardy or Levin-Cochran-Lee type inequalities has been used for the one-dimensoinal case (integrals, finite and infinite series) in a paper by the first two authors [Math. Inequal. Appl. 1, No. 4, 491-506 (1998; Zbl 0921.26015)]. Now the case of \(n\)-dimensional balls is considered, with best possible constants. The results are too complicated to be explicitely stated here.

MSC:

26D15 Inequalities for sums, series and integrals
26E60 Means

Citations:

Zbl 0921.26015
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References:

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