Open Access

On extrapolation blowups in the scale

Journal of Inequalities and Applications20062006:74960

DOI: 10.1155/JIA/2006/74960

Received: 15 October 2004

Accepted: 6 April 2005

Published: 14 March 2006

Abstract

Yano's extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator acting continuously in for close to and/or taking into as and/or with norms blowing up at speed and/or , . Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if as . The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for . We also touch the problem of comparison of results in various scales of spaces.

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Authors’ Affiliations

(1)
CNR Istituto per le Applicazioni del Calcolo "Mauro Picone"
(2)
Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università degli Studi di Napoli " Federico II"
(3)
CNR Istituto per le Applicazioni del Calcolo "Mauro Picone"
(4)
Institute of Mathematics, Academy of Sciences of the Czech Republic

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Copyright

© Claudia Capone et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.