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


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.


Authors’ Affiliations

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


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© Claudia Capone et al. 2006

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