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  • Research Article
  • Open Access

On extrapolation blowups in the scale

Journal of Inequalities and Applications20062006:74960

  • Received: 15 October 2004
  • Accepted: 6 April 2005
  • Published:


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.


  • Current Investigation
  • Maximal Function
  • Lebesgue Space
  • Stochastic Analysis
  • Boundedness Property


Authors’ Affiliations

CNR Istituto per le Applicazioni del Calcolo "Mauro Picone", Via P. Castellino 111, Napoli, 80131, Italy
Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università degli Studi di Napoli " Federico II", via Monteoliveto 3, Napoli, 80134, Italy
CNR Istituto per le Applicazioni del Calcolo "Mauro Picone", Via P. Castellino 111, Napoli, 80131, Italy
Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, Prague, 1 CZ-115 67, Czech Republic


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© Claudia Capone et al. 2006

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