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.


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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