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Publication Date:
March 2010
ISSN:
1572-9176
DOI:
10.1515/GMJ.2008.295

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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.

Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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A New Approach to the Sawyer and Sinnamon Characterizations of Hardy's Inequality for Decreasing Functions

Maria Johansson1 / Lars-Erik Persson2 / Anna Wedestig3

1Department of Mathematics, Luleå University of Technology, SE-97187 Luleå Sweden. E-mail: maria.l.johansson@ltu.se

2Department of Mathematics, Luleå University of Technology, SE-97187 Luleå Sweden. E-mail: larserik@sm.luth.se

3Department of Mathematics, Luleå University of Technology, SE-97187 Luleå Sweden. E-mail: anna.wedestig@ltu.se

Citation Information: Georgian Mathematical Journal. Volume 15, Issue 2, Pages 295–306, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2008.295, March 2010

Publication History:
Received:
2008-03-11
Published Online:
2010-03-10

Abstract

Some Hardy type inequalities for decreasing functions are characterized by one condition (Sinnamon), while others are described by two independent conditions (Sawyer). In this paper we make a new approach to deriving such results and prove a theorem, which covers both the Sinnamon result and the Sawyer result for the case where one weight is increasing. In all cases we point out that the characterizing condition is not unique and can even be chosen among some (infinite) scales of conditions.

Key words and phrases:: Inequalities; Hardy type inequalities; weights; decreasing function; scales of weight characterizations; Lorentz spaces; embeddings

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