Hardy's Inequality with Measures: The Case $0<p<1$

D. V. Prokhorov

Computer Centre Far-Eastern Branch of RAS

Abstract: In this paper, we obtain criteria for the validity of Hardy's inequality with three countably finite measures on the number line for the case $0<p<1$.

Keywords: Hardy's inequality with measures, $\sigma$-algebra, Borel subset, $\sigma$-finite measure, Hölder's inequality, Jensen's inequality, Lebesgue measure, discrete measure, Radon–Nikodym derivative.

UDC: 517

Received: 28.03.2008

DOI: 10.4213/mzm4887

 English version: Mathematical Notes, 2009, 86:6, 811–823

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