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Refined Hölder’s inequality for measurable functions. (English) Zbl 0972.26014

Summary: Let \(\nu\) be a positive measure on a space \(Y\) with \(\nu(Y)\neq 0\) and let \(f_j\) \((j= 1,2,\dots, n)\) be positive \(\nu\)-integrable functions on \(Y\). For some positive real numbers \(\alpha_j\) \((j= 1,2,\dots, n)\), \(\beta_j\) \((j= 1,2,\dots, k< n)\) and a measurable subset \(Y_1\) of \(Y\), we state some inequalities. From these results, we refine Hölder’s inequality.

MSC:

26D15 Inequalities for sums, series and integrals
28A35 Measures and integrals in product spaces
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
26E60 Means
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References:

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