IJPAM: Volume 86, No. 2 (2013)

A STRENGTHENED FORM OF A GENERAL HARDY-TYPE
INEQUALITY OBTAINED VIA SUPERQUADRATICITY
AND ITS APPLICATIONS

Aleksandra Čižmešija1, Mario Krnić2
Department of Mathematics
University of Zagreb
Bijenička cesta 30, 10000, Zagreb, CROATIA
Faculty of Electrical Engineering and Computing
University of Zagreb
Unska 3, 10000, Zagreb, CROATIA


Abstract. In this paper, we establish a new refined version of the general Hardy-type inequality utilizing the notion of superquadratic functions. The general result obtained is then applied to some particular one-dimensional and multidimensional settings providing generalizations and refinements of some well-known Hardy-type inequalities. Finally, as another consequence of the main result, we also state and prove a class of improved versions of some Hardy-Hilbert-type inequalities.

Received: September 7, 2012

AMS Subject Classification: 26D10, 26D15

Key Words and Phrases: Hardy inequality, Hardy-Hilbert inequality, Hardy-type inequalities, Hardy-Hilbert-type inequalities, non-conjugate exponents, superquadratic function, refinement, Riemann-Liouville operator, Weyl operator

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DOI: 10.12732/ijpam.v86i2.3 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 2