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Hardy's inequalities for monotone functions on partly ordered measure spaces

Published online by Cambridge University Press:  12 July 2007

Nicola Arcozzi ,
Sorina Barza ,
J. L. Garcia-Domingo  and
Javier Soria
Nicola Arcozzi
Affiliation:
Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 540127 Bologna, Italy (arcozzi@dm.unibo.it)
Sorina Barza
Affiliation:
Department of Mathematics, Karlstad University, Universitetsgatan 2, 65188 Karlstad, Sweden (sorina.barza@kau.se)
J. L. Garcia-Domingo
Affiliation:
Department of Economics, Mathematics and Computers, Universitat de Vic, 08500 Vic, Spain (jlgarcia@uvic.es)
Javier Soria
Affiliation:
Department of Applied Mathematics and Analysis, University of Barcelona, 08007 Barcelona, Spain (soria@ub.edu)
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Abstract

We characterize the weighted Hardy inequalities for monotone functions in In dimension n = 1, this recovers the standard theory of Bp weights. For n > 1, the result was previously only known for the case p = 1. In fact, our main theorem is proved in the more general setting of partly ordered measure spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 5 , October 2006 , pp. 909 - 919
Copyright
Copyright © Royal Society of Edinburgh 2006

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