On a family of means generated by the Hardy-Littlewood maximal inequality

Aleksandra Čižmešija; Iva Franjić; Josip Pečarić; Dora Pokaz

doi:10.3934/naco.2012.2.223

Article Contents

2012, Volume 2, Issue 2: 223-231. Doi: 10.3934/naco.2012.2.223

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On a family of means generated by the Hardy-Littlewood maximal inequality

1.
Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb
2.
Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb
3.
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb
4.
Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kačića Miošića 26, 10000 Zagreb

Received: October 2011

Revised: February 2012

Published: May 2012

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Abstract

The functional defined as the difference between the right-hand and the left-hand side of the Hardy-Littlewood maximal inequality is studied and its properties, such as exponential and logarithmic convexity, are explored. Furthermore, related analogues of the Lagrange and Cauchy mean value theorems are derived. Finally, using this functional, a new family of the Cauchy-type means is generated. These means are shown to be monotone.

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Mathematics Subject Classification: Primary: 26D10; Secondary 26D15.

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